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Integral Transforms and Special Functions Volume 7, 1998 - Issue 3-4
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Original Articles

Convolution and potential type operators in Lp(x)(Rn)

Stefan G. Samko Unidade do Algarve, UCEH, Gambelas, FARO 8000, Portugal
Pages 261-284 | Received 14 Dec 1996, Published online: 03 Apr 2007

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Canay Aykol, Xayyam A. Badalov & Javanshir J. Hasanov. (2020) Maximal and singular operators in the local “complementary” generalized variable exponent Morrey spaces on unbounded sets. Quaestiones Mathematicae 43:10, pages 1487-1512.
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L. Diening, P. Nägele & M. Růžička. (2012) Monotone operator theory for unsteady problems in variable exponent spaces. Complex Variables and Elliptic Equations 57:11, pages 1209-1231.
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L. Diening, D. Lengeler & M. Růžička. (2011) The Stokes and Poisson problem in variable exponent spaces. Complex Variables and Elliptic Equations 56:7-9, pages 789-811.
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Vakhtang Kokilashvili & Alexander Meskhi. (2010) Maximal functions and potentials in variable exponent Morrey spaces with non-doubling measure. Complex Variables and Elliptic Equations 55:8-10, pages 923-936.
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Muhammad Asif, Vakhtang Kokilashvili & Alexander Meskhi. (2009) Boundedness criteria for maximal functions and potentials on the half-space in weighted Lebesgue spaces with variable exponents. Integral Transforms and Special Functions 20:11, pages 805-819.
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Vakhtang Kokilashvili & Alexander Meskhi. (2007) Weighted criteria for generalized fractional maximal functions and potentials in Lebesgue spaces with variable exponent. Integral Transforms and Special Functions 18:9, pages 609-628.
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S. Samko. (2005) On a progress in the theory of lebesgue spaces with variable exponent: maximal and singular operators. Integral Transforms and Special Functions 16:5-6, pages 461-482.
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Vasily E. Tarasov. (2023) General Fractional Calculus in Multi-Dimensional Space: Riesz Form. Mathematics 11:7, pages 1651.
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Babar Sultan, Fatima Azmi, Mehvish Sultan, Mazhar Mehmood & Nabil Mlaiki. (2022) Boundedness of Riesz Potential Operator on Grand Herz-Morrey Spaces. Axioms 11:11, pages 583.
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Canay Aykol, Xayyam A. Badalov & Javanshir J. Hasanov. (2020) Boundedness of the potential operators and their commutators in the local “complementary” generalized variable exponent Morrey spaces on unbounded sets. Annals of Functional Analysis 11:2, pages 423-438.
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Stefan Samko. (2020) Variable exponent fractional integrals in the limiting case α( x ) p ( n ) ≡ n on quasimetric measure spaces . Georgian Mathematical Journal 27:1, pages 157-164.
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Claudianor O. Alves & Leandro S. Tavares. (2019) A Hardy–Littlewood–Sobolev-Type Inequality for Variable Exponents and Applications to Quasilinear Choquard Equations Involving Variable Exponent. Mediterranean Journal of Mathematics 16:2.
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Alexander Meskhi, Humberto Rafeiro & Muhammad Asad Zaighum. (2019) On the boundedness of Marcinkiewicz integrals on continual variable exponent Herz spaces. Georgian Mathematical Journal 26:1, pages 105-116.
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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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J.-L. Wu. (2018) Boundedness of Riesz-Type Potential Operators on Variable Exponent Herz–Morrey Spaces. Ukrainian Mathematical Journal 69:9, pages 1379-1392.
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Yakhshiboev Makhmadiyor. 2018. Differential Equations and Dynamical Systems. Differential Equations and Dynamical Systems 183 195 .
Kwok-Pun HO. (2017) Fractional integral operators with homogeneous kernels on Morrey spaces with variable exponents. Journal of the Mathematical Society of Japan 69:3.
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Jiang-Long Wu & Wen-Jiao Zhao. (2016) Boundedness for fractional Hardy-type operator on variable-exponent Herz–Morrey spaces. Kyoto Journal of Mathematics 56:4.
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Vasily E. Tarasov. (2016) Partial fractional derivatives of Riesz type and nonlinear fractional differential equations. Nonlinear Dynamics 86:3, pages 1745-1759.
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Rafeiro Humberto & Stefan Samko. (2016) Fractional Integrals and Derivatives: Mapping Properties. Fractional Calculus and Applied Analysis 19:3, pages 580-607.
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Pinhong Long & Huili Han. (2016) Characterizations of some operators on the vanishing generalized Morrey spaces with variable exponent. Journal of Mathematical Analysis and Applications 437:1, pages 419-430.
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Canqin Tang, Qing Wu & Jingshi Xu. (2016) Estimates of Fractional Integral Operators on Variable Exponent Lebesgue Spaces. Journal of Function Spaces 2016, pages 1-7.
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Sun-Sig Byun & Jihoon Ok. (2016) Optimal Gradient Estimates for Parabolic Equations in Variable Exponent Spaces. International Mathematics Research Notices 2016:8, pages 2493-2521.
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Jichang Kuang. 2016. Contributions in Mathematics and Engineering. Contributions in Mathematics and Engineering 353 375 .
Rene Erlin Castillo & Humberto RafeiroRené Erlín Castillo & Humberto Rafeiro. 2016. An Introductory Course in Lebesgue Spaces. An Introductory Course in Lebesgue Spaces 331 358 .
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Sun-Sig Byun, Mikyoung Lee & Jihoon Ok. (2015) $$W^{2,p(\cdot )}$$ W 2 , p ( · ) -regularity for elliptic equations in nondivergence form with BMO coefficients. Mathematische Annalen 363:3-4, pages 1023-1052.
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A. Almeida, P. Harjulehto, P. Hästö & T. Lukkari. (2013) Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces. Annali di Matematica Pura ed Applicata (1923 -) 194:2, pages 405-424.
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Humberto Rafeiro & Stefan Samko. (2015) Riesz potential operator in continual variable exponents Herz spaces. Mathematische Nachrichten 288:4, pages 465-475.
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Vakhtang Kokilashvili & Alexander Meskhi. (2014) Two-weight norm estimates for sublinear integral operators in variable exponent Lebesgue spaces. Studia Scientiarum Mathematicarum Hungarica 51:3, pages 384-406.
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Jianglong Wu. (2014) BOUNDEDNESS FOR FRACTIONAL HARDY-TYPE OPERATOR ON HERZ-MORREY SPACES WITH VARIABLE EXPONENT. Bulletin of the Korean Mathematical Society 51:2, pages 423-435.
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Vakhtang Kokilashvili, Alexander Meskhi & Muhammad Asad Zaighum. (2013) Weighted kernel operators in variable exponent amalgam spaces. Journal of Inequalities and Applications 2013:1.
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Vakhtang Kokilashvili, Alexander Meskhi & Muhammad Asad Zaighum. (2013) Positive kernel operators in $$L^{p(x)}$$ spaces. Positivity 17:4, pages 1123-1140.
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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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V. S. Guliyev & S. G. Samko. (2013) Maximal, Potential, and Singular Operators in the Generalized Variable Exponent Morrey Spaces on Unbounded Sets. Journal of Mathematical Sciences 193:2, pages 228-248.
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M. Ramseyer, O. Salinas & B. Viviani. (2013) Lipschitz type smoothness of the fractional integral on variable exponent spaces. Journal of Mathematical Analysis and Applications 403:1, pages 95-106.
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Stefan Samko. (2013) A note on Riesz fractional integrals in the limiting case α(x)p(x) ≡ n. Fractional Calculus and Applied Analysis 16:2, pages 370-377.
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Vagif S. Guliyev, Javanshir J. Hasanov & Stefan G. Samko. (2013) Maximal, potential and singular operators in the local “complementary” variable exponent Morrey type spaces. Journal of Mathematical Analysis and Applications 401:1, pages 72-84.
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Stefan Samko. (2012) Fractional integration and differentiation of variable order: an overview. Nonlinear Dynamics 71:4, pages 653-662.
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David V. Cruz-Uribe & Alberto FiorenzaDavid V. Cruz-Uribe & Alberto Fiorenza. 2013. Variable Lebesgue Spaces. Variable Lebesgue Spaces 191 237 .
David V. Cruz-Uribe & Alberto FiorenzaDavid V. Cruz-Uribe & Alberto Fiorenza. 2013. Variable Lebesgue Spaces. Variable Lebesgue Spaces 1 12 .
Sergei V. Rogosin. 2013. Advances in Harmonic Analysis and Operator Theory. Advances in Harmonic Analysis and Operator Theory 49 63 .
V. Kokilashvili. 2013. Advances in Harmonic Analysis and Operator Theory. Advances in Harmonic Analysis and Operator Theory 1 48 .
Alexandre Almeida & Douadi Drihem. (2012) Maximal, potential and singular type operators on Herz spaces with variable exponents. Journal of Mathematical Analysis and Applications 394:2, pages 781-795.
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Joaquín Motos, María Jesús Planells & César F. Talavera. (2012) On variable exponent Lebesgue spaces of entire analytic functions. Journal of Mathematical Analysis and Applications 388:2, pages 775-787.
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Mubariz G. Hajibayov & Stefan Samko. (2011) Generalized potentials in variable exponent Lebesgue spaces on homogeneous spaces. Mathematische Nachrichten 284:1, pages 53-66.
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Mitsuo Izuki. (2010) Commutators of fractional integrals on Lebesgue and Herz spaces with variable exponent. Rendiconti del Circolo Matematico di Palermo 59:3, pages 461-472.
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V. S. Guliyev, J. J. Hasanov & S. G. Samko. (2010) Boundedness of maximal, potential type, and singular integral operators in the generalized variable exponent Morrey type spaces. Journal of Mathematical Sciences 170:4, pages 423-443.
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Xianling Fan. (2010) Variable exponent Morrey and Campanato spaces. Nonlinear Analysis: Theory, Methods & Applications 72:11, pages 4148-4161.
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Vakhtang Kokilashvili, Alexander Meskhi & Muhammad Sarwar. (2010) Potential Operators in Variable Exponent Lebesgue Spaces: Two-Weight Estimates. Journal of Inequalities and Applications 2010:1, pages 329571.
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Mubariz G. Hajibayov & Stefan G. Samko. 2010. Recent Trends in Toeplitz and Pseudodifferential Operators. Recent Trends in Toeplitz and Pseudodifferential Operators 107 122 .
Yongqiang Fu. (2009) The principle of concentration compactness in spaces and its application. Nonlinear Analysis: Theory, Methods & Applications 71:5-6, pages 1876-1892.
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Alexandre Almeida & Stefan Samko. (2009) Fractional and Hypersingular Operators in Variable Exponent Spaces on Metric Measure Spaces. Mediterranean Journal of Mathematics 6:2, pages 215-232.
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Stefan Samko. 2009. Analysis, Partial Differential Equations and Applications. Analysis, Partial Differential Equations and Applications 281 301 .
V. Kokilashvili & S. Samko. (2008) Boundedness of maximal operators and potential operators on Carleson curves in Lebesgue spaces with variable exponent. Acta Mathematica Sinica, English Series 24:11, pages 1775-1800.
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David E. Edmunds, Vakhtang Kokilashvili & Alexander Meskhi. (2008) One‐sided operators in L p ( x ) spaces . Mathematische Nachrichten 281:11, pages 1525-1548.
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Xianling Fan. (2008) Boundary trace embedding theorems for variable exponent Sobolev spaces. Journal of Mathematical Analysis and Applications 339:2, pages 1395-1412.
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N.G. Samko, S.G. Samko & B.G. Vakulov. (2007) Weighted Sobolev theorem in Lebesgue spaces with variable exponent. Journal of Mathematical Analysis and Applications 335:1, pages 560-583.
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D. Cruz‐UribeSFOSFO & A. Fiorenza. (2007) Approximate identities in variable L p spaces . Mathematische Nachrichten 280:3, pages 256-270.
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S. Samko, E. Shargorodsky & B. Vakulov. (2007) Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, II. Journal of Mathematical Analysis and Applications 325:1, pages 745-751.
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Yoshihiro Mizuta & Tetsu Shimomura. (2005) Sobolev's inequality for Riesz potentials with variable exponent satisfying a log-Hölder condition at infinity. Journal of Mathematical Analysis and Applications 311:1, pages 268-288.
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S. Samko & B. Vakulov. (2005) Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators. Journal of Mathematical Analysis and Applications 310:1, pages 229-246.
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Jan Chabrowski & Yongqiang Fu. (2005) Existence of solutions for -Laplacian problems on a bounded domain . Journal of Mathematical Analysis and Applications 306:2, pages 604-618.
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Lars Diening. (2004) Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces L p (·) and W k,p (·) . Mathematische Nachrichten 268:1, pages 31-43.
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