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Original Articles

Fractional Integration, morrey spaces and a schrödinger equation

Pages 2005-2055 | Published online: 18 Nov 2011

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A. Kucukaslan, V. S. Guliyev, C. Aykol & A. Serbetci. (2023) Maximal and Calderón–Zygmund operators on the local variable Morrey–Lorentz spaces and some applications. Applicable Analysis 102:2, pages 406-415.
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Mike O'Leary. (2003) Conditions for the Local Boundedness of Solutions of the Navier–Stokes System in Three Dimensions. Communications in Partial Differential Equations 28:3-4, pages 617-636.
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Articles from other publishers (49)

Vagif S. Guliyev. (2024) Characterizations of Lipschitz functions via the commutators of maximal function in total Morrey spaces. Mathematical Methods in the Applied Sciences.
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Loukas Grafakos & Alexander Meskhi. (2022) On Sharp Olsen’s and Trace Inequalities for Multilinear Fractional Integrals. Potential Analysis 59:3, pages 1039-1050.
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Muhamad Jamaludin, Daniel Salim & Denny Ivanal Hakim. (2023) Some Applications of $$L^1$$-Estimates of Fractional Integral Operators in Lorentz Spaces. Bulletin of the Malaysian Mathematical Sciences Society 46:5.
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Suting Zheng, Dinghuai Wang & Xi Hu. (2023) Sharp bounds for multilinear fractional integral operators on Morrey type spaces: the endpoint cases. Positivity 27:3.
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Kwok-Pun Ho. (2023) Fractional integral operators on Morrey spaces built on rearrangement-invariant quasi-Banach function spaces. Positivity 27:2.
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Erlan D. Nursultanov & Durvudkhan Suragan. (2022) On the convolution operator in Morrey spaces. Journal of Mathematical Analysis and Applications 515:1, pages 126357.
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Yao Yang & Junming Liu. (2022) Integral Operators on Bergman–Morrey Spaces. The Journal of Geometric Analysis 32:6.
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Gael Diebou Yomgne. (2022) Nonlinear biharmonic equation in half-space with rough Neumann boundary data and potentials. Nonlinear Analysis 215, pages 112623.
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Yuxing Guo. (2021) Generalized Olsen inequality and Schrödinger type elliptic equations. Georgian Mathematical Journal 28:2, pages 233-239.
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Qianjun He & Dunyan Yan. (2020) Bilinear fractional integral operators on Morrey spaces. Positivity 25:2, pages 399-429.
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Yoshihiro Sawano & Satoko Sugano. (2020) Complex Interpolation and the Adams Theorem. Potential Analysis 54:2, pages 299-305.
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Takeshi Iida. (2020) Orlicz-fractional maximal operators in Morrey and Orlicz–Morrey spaces. Positivity 25:1, pages 243-272.
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Liguang Liu, Chengjun Yue & Lunchuan Zhang. (2021) Restricting Riesz-logarithmic-Besov potentials. Journal of Mathematical Analysis and Applications 493:2, pages 124572.
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Fatih Deringoz. 2021. Operator Theory and Harmonic Analysis. Operator Theory and Harmonic Analysis 143 159 .
Idha Sihwaningrum, Sri Maryani & Hendra Gunawan. (2020) Extension of Hardy–Littlewood–Sobolev Inequalities for Riesz Potentials on Hypergroups. Mediterranean Journal of Mathematics 17:6.
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Hua Wang. (2020) Semigroup Maximal Functions, Riesz Transforms, and Morrey Spaces Associated with Schrödinger Operators on the Heisenberg Groups. Journal of Function Spaces 2020, pages 1-22.
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Qifeng Zhang, Xiaoman Lin, Kejia Pan & Yunzhu Ren. (2020) Linearized ADI schemes for two-dimensional space-fractional nonlinear Ginzburg–Landau equation. Computers & Mathematics with Applications 80:5, pages 1201-1220.
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Dorothee D. Haroske & Leszek Skrzypczak. (2019) Morrey Sequence Spaces: Pitt’s Theorem and Compact Embeddings. Constructive Approximation 51:3, pages 505-535.
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Dorothee D. Haroske, Susana D. Moura & Leszek Skrzypczak. (2020) Some Embeddings of Morrey Spaces with Critical Smoothness. Journal of Fourier Analysis and Applications 26:3.
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N. Hatano. (2020) Fractional Operators on Morrey—Lorentz Spaces and the Olsen Inequality. Mathematical Notes 107:1-2, pages 63-79.
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Kwok-Pun Ho. (2018) Weak Type Estimates of the Fractional Integral Operators on Morrey Spaces with Variable Exponents. Acta Applicandae Mathematicae 159:1, pages 1-10.
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HENDRA GUNAWAN, DENNY IVANAL HAKIM, EIICHI NAKAI & YOSHIHIRO SAWANO. (2018) THE HARDY AND HEISENBERG INEQUALITIES IN MORREY SPACES. Bulletin of the Australian Mathematical Society 97:3, pages 480-491.
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Idha Sihwaningrum, Hendra Gunawan & Eiichi Nakai. (2018) Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces. Mathematische Nachrichten 291:8-9, pages 1400-1417.
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Shohei Nakamura, Yoshihiro Sawano & Hitoshi Tanaka. (2017) The Fractional Operators on Weighted Morrey Spaces. The Journal of Geometric Analysis 28:2, pages 1502-1524.
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L. Liu & J. Xiao. (2017) Restricting Riesz–Morrey–Hardy potentials. Journal of Differential Equations 262:11, pages 5468-5496.
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Yanlong Shi, Zengyan Si, Xiangxing Tao & Yafeng Shi. (2016) Necessary and sufficient conditions for boundedness of multilinear fractional integrals with rough kernels on Morrey type spaces. Journal of Inequalities and Applications 2016:1.
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Vagif S. Guliyev, Sabir G. Hasanov, Yoshihiro Sawano & Takahiro Noi. (2016) Non-smooth Atomic Decompositions for Generalized Orlicz–Morrey Spaces of the Third Kind. Acta Applicandae Mathematicae 145:1, pages 133-174.
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Pierre Lemarie-Rieusset. 2016. The Navier-Stokes Problem in the 21st Century. The Navier-Stokes Problem in the 21st Century 677 708 .
Zhiheng Wang & Zengyan Si. (2015) Necessary and sufficient conditions for the boundedness of rough multilinear fractional operators on Morrey-type spaces. Journal of Inequalities and Applications 2015:1.
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Yoshihiro Sawano, Denny Ivanal Hakim & Hendra Gunawan. (2015) Non‐smooth atomic decomposition for generalized Orlicz‐Morrey spaces. Mathematische Nachrichten 288:14-15, pages 1741-1775.
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Junming Liu & Zengjian Lou. (2015) Properties of analytic Morrey spaces and applications. Mathematische Nachrichten 288:14-15, pages 1673-1693.
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Wen Yuan, Dorothee D. Haroske, Susana D. Moura, Leszek Skrzypczak & Dachun Yang. (2015) Limiting embeddings in smoothness Morrey spaces, continuity envelopes and applications. Journal of Approximation Theory 192, pages 306-335.
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PengTao Li, JunMing Liu & ZengJian Lou. (2014) Integral operators on analytic Morrey spaces. Science China Mathematics 57:9, pages 1961-1974.
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Takeshi Iida. (2014) WEIGHTED INEQUALITIES ON MORREY SPACES FOR LINEAR AND MULTILINEAR FRACTIONAL INTEGRALS WITH HOMOGENEOUS KERNELS. Taiwanese Journal of Mathematics 18:1.
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Yoshihiro Sawano. (2013) Atomic Decompositions of Hardy Spaces with Variable Exponents and its Application to Bounded Linear Operators. Integral Equations and Operator Theory 77:1, pages 123-148.
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Hitoshi Tanaka & Hendra Gunawan. (2012) The Local Trace Inequality for Potential Type Integral Operators. Potential Analysis 38:2, pages 653-681.
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Yoshihiro Sawano & Tetsu Shimomura. (2013) Sobolev Embeddings for Generalized Riesz Potentials of Functions in Morrey Spaces over Nondoubling Measure Spaces. Journal of Function Spaces and Applications 2013, pages 1-12.
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Humberto Rafeiro, Natasha Samko & Stefan Samko. 2013. Operator Theory, Pseudo-Differential Equations, and Mathematical Physics. Operator Theory, Pseudo-Differential Equations, and Mathematical Physics 293 323 .
Takeshi Iida, Enji Sato, Yoshihiro Sawano & Hitoshi Tanaka. (2012) Multilinear fractional integrals on Morrey spaces. Acta Mathematica Sinica, English Series 28:7, pages 1375-1384.
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Takeshi Iida, Enji Sato, Yoshihiro Sawano & Hitoshi Tanaka. (2011) Sharp bounds for multilinear fractional integral operators on Morrey type spaces. Positivity 16:2, pages 339-358.
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Yoshihiro Sawano, Satoko Sugano & Hitoshi Tanaka. (2011) Orlicz–Morrey Spaces and Fractional Operators. Potential Analysis 36:4, pages 517-556.
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Igor Kukavica. (2011) Partial regularity for the Navier–Stokes equations with a force in a Morrey space. Journal of Mathematical Analysis and Applications 374:2, pages 573-584.
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Yoshihiro MIZUTA, Eiichi NAKAI, Takao OHNO & Tetsu SHIMOMURA. (2010) Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials. Journal of the Mathematical Society of Japan 62:3.
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HITOSHI TANAKA. (2010) MORREY SPACES AND FRACTIONAL OPERATORS. Journal of the Australian Mathematical Society 88:2, pages 247-259.
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H. GUNAWAN, Y. SAWANO & I. SIHWANINGRUM. (2009) FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES. Bulletin of the Australian Mathematical Society 80:2, pages 324-334.
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Hendra Gunawan & Eridani Eridani. (2009) Fractional Integrals and Generalized Olsen Inequalities. Kyungpook mathematical journal 49:1, pages 31-39.
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Yoshihiro Sawano, Satoko Sugano & Hitoshi Tanaka. (2009) A Note on Generalized Fractional Integral Operators on Generalized Morrey Spaces. Boundary Value Problems 2009, pages 1-18.
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Kazuhiro Kurata, Seiichi Nishigaki & Satoko Sugano. (1999) Boundedness of integral operators on generalized Morrey spaces and its application to Schrödinger operators. Proceedings of the American Mathematical Society 128:4, pages 1125-1134.
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Tian Lixin & Liu Zengrong. (1998) The Schrödinger operator. Proceedings of the American Mathematical Society 126:1, pages 203-211.
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