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Applicable Analysis
An International Journal
Volume 7, 1978 - Issue 3
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Original Articles

On singular integrals with variable kernels

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Pages 221-238 | Published online: 13 May 2010

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Lung-kee Chen. (1988) The singular integrals related to the calderón-zygmund method of rotations. Applicable Analysis 30:4, pages 319-329.
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Articles from other publishers (76)

Yanping Chen & Zihua Guo. (2024) Uniform sparse domination and quantitative weighted boundedness for singular integrals and application to the dissipative quasi-geostrophic equation. Journal of Differential Equations 378, pages 871-917.
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Yanping Chen, Zihua Guo & Tian Tian. (2023) A uniform Besov boundedness and the well-posedness of the generalized dissipative quasi-geostrophic equation in the critical Besov space. Forum Mathematicum 0:0.
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Kazuaki Taira. (2023) Singular integrals and Feller semigroups with jump phenomena. Rendiconti del Circolo Matematico di Palermo Series 2.
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Hugo Aimar, Raquel Crescimbeni & Luis Nowak. (2023) Singular Integrals with Variable Kernels in Dyadic Settings. Acta Mathematica Sinica, English Series.
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Yanping Chen & Zhenbing Gong. (2022) Variational inequalities for hypersingular integrals with variable kernels. Rocky Mountain Journal of Mathematics 52:2.
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Teng Wang & Yanping Chen. (2022) Quantitative weighted bounds for singular integrals and fractional differentiations. Analysis and Mathematical Physics 12:2.
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Alexander V. Vasilyev, Vladimir B. Vasilyev & Oksana A. Tarasova. (2022) Frames of solutions and discrete analysis of pseudo‐differential equations. Mathematical Methods in the Applied Sciences.
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Xukui Shao & Shuangping Tao. (2021) Weighted Estimates of Variable Kernel Fractional Integral and Its Commutators on Vanishing Generalized Morrey Spaces with Variable Exponent. Chinese Annals of Mathematics, Series B 42:3, pages 451-470.
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Zhenbing Gong, Yanping Chen & Wenyu Tao. (2021) Jump and variational inequalities for averaging operators with variable kernels. Communications on Pure & Applied Analysis 20:5, pages 1851.
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Yanping Chen, Yong Ding & Kai Zhu. (2020) L2L^{2} boundedness for commutators of fractional differential type Marcinkiewicz integral with rough variable kernel and BMO Sobolev spaces. Georgian Mathematical Journal 27:4, pages 529-540.
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Latifa Debbi. (2020) Fractional Stochastic Active Scalar Equations Generalizing the Multi-Dimensional Quasi-Geostrophic & 2D-Navier–Stokes Equations: The General Case. Journal of Mathematical Fluid Mechanics 22:4.
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Dazhao Chen. (2020) Weighted boundedness for Toeplitz type operator related to singular integral transform with variable Calderón-Zygmund kernel. AIMS Mathematics 6:1, pages 688-697.
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Dazhao Chen. (2019) Weighted boundedness for Toeplitz type operator associated to singular integral operator with variable Calderón-Zygmund kernel. Hacettepe Journal of Mathematics and Statistics, pages 1-12.
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Andrea Scapellato. (2019) Regularity of solutions to elliptic equations on Herz spaces with variable exponents. Boundary Value Problems 2019:1.
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Xukui Shao & Shuangping Tao. (2019) Weak Type Estimates of Variable Kernel Fractional Integral and Their Commutators on Variable Exponent Morrey Spaces. Journal of Function Spaces 2019, pages 1-11.
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Yanxiang Tan & Lanzhe Liu. (2018) Boundedness of Toeplitz operators related to singular integral operators. Izvestiya: Mathematics 82:6, pages 1225-1238.
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Yanping Chen & Liwei Wang. (2018) L2(ℝn) boundedness for Calderón commutator with rough variable kernel. Frontiers of Mathematics in China 13:5, pages 1013-1031.
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Lin Tang. (2018) The estimates of Bessel integrals with oscillatory factors. Mathematische Nachrichten 291:8-9, pages 1418-1436.
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Yanqi Yang & Shuangping Tao. (2018) Singular integrals with variable kernel and fractional differentiation in homogeneous Morrey-Herz-type Hardy spaces with variable exponents. Open Mathematics 16:1, pages 326-345.
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Янсян Тан, Yanxiang Tan, Ляньчже Лю & Lanzhe Liu. (2018) Ограниченность операторов Теплица, связанных с сингулярными интегральными операторамиBoundedness of Toeplitz operators related to singular integral operators. Известия Российской академии наук. Серия математическая Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya 82:6, pages 158-171.
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Andrea Scapellato. (2018) Homogeneous Herz spaces with variable exponents and regularity results. Electronic Journal of Qualitative Theory of Differential Equations:82, pages 1-11.
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Omer Abdalrhman, Afif Abdalmonem & Shuangping Tao. (2017) Boundedness of Calderón-Zygmund Operator and Their Commutator on Herz Spaces with Variable Exponent. Applied Mathematics 08:04, pages 428-443.
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Yanqi Yang & Shuangping Tao. (2017) Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces. Journal of Function Spaces 2017, pages 1-10.
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Yanping Chen, Yong Ding & Guixiang Hong. (2016) Commutators with fractional differentiation and new characterizations of BMO-Sobolev spaces. Analysis & PDE 9:6, pages 1497-1522.
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Yanxiang Tan & Lanzhe Liu. (2016) Weighted boundedness of multilinear operator associated to singular integral operator with variable Calderón–Zygmund Kernel. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas.
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Hua Wang. (2016) Estimates of some integral operators with bounded variable kernels on the hardy and weak hardy spaces over ℝ n. Acta Mathematica Sinica, English Series 32:4, pages 411-438.
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Afif Abdalmonem, Omer Abdalrhman & Shuangping Tao. (2016) The Boundedness of Fractional Integral with Variable Kernel on Variable Exponent Herz-Morrey Spaces. Journal of Applied Mathematics and Physics 04:04, pages 787-795.
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Afif Abdalmonem, Omer Abdalrhman & Shuangping Tao. (2016) Boundedness of Fractional Integral with Variable Kernel and Their Commutators on Variable Exponent Herz Spaces. Applied Mathematics 07:10, pages 1165-1182.
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秋阅 万. (2016) The Boundedness of Multilinear Fractional Integral Operators with Variable Kernel on Variable Exponent Lebesgue Spaces. Pure Mathematics 06:01, pages 72-80.
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Jiecheng Chen, Yanping Chen & Guoen Hu. (2015) Compactness for the commutators of singular integral operators with rough variable kernels. Journal of Mathematical Analysis and Applications 431:1, pages 597-621.
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Yanping Chen & Yong Ding. (2015) Sharp bounds for the commutators with variable kernels of fractional differentiations and BMO Sobolev spaces. Nonlinear Analysis: Theory, Methods & Applications 116, pages 85-99.
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Yanping Chen & Kai Zhu. (2015) Weighted norm inequality for the singular integral with variable kernel and fractional differentiation. Journal of Mathematical Analysis and Applications 423:2, pages 1610-1629.
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Hua Wang. (2014) Boundedness of Singular Integral Operators with Variable Kernels on Weighted Weak Hardy Spaces. Chinese Journal of Mathematics 2014, pages 1-6.
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Alexander Vasilyev & Vladimir Vasilyev. (2013) Approximation rate and invertibility for some singular integral operators. PAMM 13:1, pages 373-374.
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HUA WANG. (2013) BOUNDEDNESS OF SEVERAL INTEGRAL OPERATORS WITH BOUNDED VARIABLE KERNELS ON HARDY AND WEAK HARDY SPACES. International Journal of Mathematics 24:12, pages 1350095.
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Honghai Liu. (2013) Carleson-type maximal operators with variable kernels. Chinese Annals of Mathematics, Series B 34:6, pages 855-860.
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Hui-Ling Wu & Jia-Cheng Lan. (2013) Lipschitz Estimates for Fractional Multilinear Singular Integral on Variable Exponent Lebesgue Spaces. Abstract and Applied Analysis 2013, pages 1-6.
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Yanping Chen, Yong Ding & Ran Li. (2011) The Boundedness for Commutator of Fractional Integral Operator With Rough Variable Kernel. Potential Analysis 38:1, pages 119-142.
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Javier Duoandikoetxea & Virginia Naibo. 2013. Excursions in Harmonic Analysis, Volume 2. Excursions in Harmonic Analysis, Volume 2 211 228 .
DAH-CHIN LUOR. (2012) MIXED NORM INEQUALITIES FOR SOME DIRECTIONAL MAXIMAL OPERATORS. Bulletin of the Australian Mathematical Society 86:3, pages 448-455.
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Yanping Chen, Yong Ding & Ran Li. (2011) The boundedness for commutators of a class of maximal hypersingular integrals with variable kernels. Nonlinear Analysis: Theory, Methods & Applications 74:15, pages 4918-4940.
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Yanping Chen & Ding Yong. (2011) boundedness for Littlewood–Paley operators with rough variable kernels . Journal of Mathematical Analysis and Applications 377:2, pages 889-904.
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Yandan Zhang, Dashan Fan & Jiecheng Chen. (2010) Transference on some non-convolution operators from euclidean spaces to torus. Chinese Annals of Mathematics, Series B 32:1, pages 59-68.
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Yanping Chen & Yong Ding. (2010) Boundedness for commutator of rough hypersingular integrals with variable kernels. Michigan Mathematical Journal 59:1.
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Maria Alessandra Ragusa. (2009) Homogeneous Herz spaces and regularity results. Nonlinear Analysis: Theory, Methods & Applications 71:12, pages e1909-e1914.
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Hui Wang & Chun-jie Zhang. (2009) A note on parameterized Marcinkiewicz integrals with variable kernels. Applied Mathematics-A Journal of Chinese Universities 24:3, pages 315-320.
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Yan Ping Chen. (2009) Boundedness of the commutator of Marcinkiewicz integral with rough variable kernel. Acta Mathematica Sinica, English Series 25:6, pages 983-1000.
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Qingying Xue & Kôzô Yabuta. (2009) On the boundedness of singular integrals with variable kernels. Tohoku Mathematical Journal 61:1.
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Chin-Cheng Lin, Ying-Chieh Lin, Xiangxing Tao & Xiao Yu. (2009) The boundedness of Marcinkiewicz integral with variable kernel. Illinois Journal of Mathematics 53:1.
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Ming-Yi Lee, Chin-Cheng Lin, Ying-Chieh Lin & Dunyan Yan. (2008) Boundedness of singular integral operators with variable kernels. Journal of Mathematical Analysis and Applications 348:2, pages 787-796.
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Neal Bez. (2008) Mixed-norm estimates for a class of nonisotropic directional maximal operators and Hilbert transforms. Journal of Functional Analysis 255:12, pages 3281-3302.
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Jie-cheng Chen, Xiao Yu, Yan-dan Zhang & Hui Wang. (2008) Hypersingular parameterized Marcinkiewicz integrals with variable kernels on Sobolev and Hardy-Sobolev spaces. Applied Mathematics-A Journal of Chinese Universities 23:4, pages 420-430.
Crossref
Xiaomei Wu. (2008) Boundedness of Marcinkiewicz integral related to multilinear commutators with variable kernels on Hardy spaces. Analysis in Theory and Applications 24:2, pages 139-148.
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Yong Ding & Ran Li. (2008) An integral estimate of Bessel function and its application. Science in China Series A: Mathematics 51:5, pages 897-906.
Crossref
Shanzhen Lu. (2007) Marcinkiewicz integral with rough kernels. Frontiers of Mathematics in China 3:1, pages 1-14.
Crossref
Xiangxing Tao, Xiao Yu & Songyan Zhang. (2008) Boundedness on Hardy-Sobolev Spaces for Hypersingular Marcinkiewicz Integrals with Variable Kernels. Journal of Inequalities and Applications 2008:1, pages 835938.
Crossref
Daning Chen, Yong Ding & Dashan Fan. (2008) Operators with rough singular kernels. Journal of Mathematical Analysis and Applications 337:2, pages 906-918.
Crossref
Qingying Xue & Kôzô Yabuta. (2007) L2-Boundedness of Marcinkiewicz Integrals along Surfaces with Variable Kernels: Another Sufficient Condition. Journal of Inequalities and Applications 2007, pages 1-15.
Crossref
Chen Jiecheng & You Ying. (2006) Rough hypersingular integral operators with an oscillating factor. Applied Mathematics-A Journal of Chinese Universities 21:2, pages 179-190.
Crossref
Yong Ding, Shanzhen Lu & Shuanglin Shao. (2006) Integral operators with variable kernels on weak Hardy spaces. Journal of Mathematical Analysis and Applications 317:1, pages 127-135.
Crossref
Jiecheng Chen, Yong Ding & Dashan Fan. (2006) Littlewood-Paley operators with variable kernels. Science in China Series A 49:5, pages 639-650.
Crossref
Zheng Yang & Jiacheng Lan. (2006) The fractional multilinear singular integral with variable kernels on hardy spaces. Analysis in Theory and Applications 22:1, pages 81-90.
Crossref
Pu Zhang & Kai Zhao. (2005) Commutators of integral operators with variable kernels on Hardy spaces. Proceedings Mathematical Sciences 115:4, pages 399-410.
Crossref
O. A. Ladyzhenskaya. (2005) Construction of Bases in Spaces of Solenoidal Vector Fields. Journal of Mathematical Sciences 130:4, pages 4827-4835.
Crossref
Daning Chen, Jiecheng Chen & Dashan Fan. (2005) Rough singular integral operators on Hardy-Sobolev spaces. Applied Mathematics-A Journal of Chinese Universities 20:1, pages 1-9.
Crossref
Tang Lin & Yang Dachun. (2003) Oscillatory singular integrals with variable rough kernel, II. Analysis in Theory and Applications 19:1, pages 1-13.
Crossref
Lin Tang & Dachun Yang. (2002) Boundedness of singular integrals of variable rough Calder�n-Zygmund kernels along surfaces. Integral Equations and Operator Theory 43:4, pages 488-502.
Crossref
Shanzhen Lu, Dachun Yang & Zusheng Zhou. (1999) On local oscillatory integrals with variable Calder�n-Zygmund kernels. Integral Equations and Operator Theory 33:4, pages 456-470.
Crossref
Shanzhen Lu, Dachun Yang & Zusheng Zhou. (1999) On local oscillatory integrals with variable Calder�n-Zygmund kernels, II. Integral Equations and Operator Theory 34:1, pages 56-64.
Crossref
Steve Hofmann. (1997) Parabolic singular integrals of Calderón-type, rough operators, and caloric layer potentials. Duke Mathematical Journal 90:2.
Crossref
Eugene Shargorodsky. (2006) Some Remarks on the Boundedness of Pseudodifferential Operators. Mathematische Nachrichten 183:1, pages 229-273.
Crossref
S. Prössdorf. 1991. Analysis IV. Analysis IV 1 125 .
Rolf Leis. 1990. Ein Jahrhundert Mathematik 1890–1990. Ein Jahrhundert Mathematik 1890–1990 491 535 .
Michael Christ, Javier Duoandikoetxea & José L. Rubio de Francia. (1986) Maximal operators related to the Radon transform and the Calderon-Zygmund method of rotations. Duke Mathematical Journal 53:1.
Crossref
. 1986. 446 456 .
E. M. Dyn'kin & B. P. Osilenker. (1985) Weighted estimates of singular integrals and their applications. Journal of Soviet Mathematics 30:3, pages 2094-2154.
Crossref

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