Boundedness of multilinear singular integrals on central Morrey spaces with variable exponents

Hongbin WANG , Jingshi XU , Jian TAN

Front. Math. China ›› 2020, Vol. 15 ›› Issue (5) : 1011 -1034.

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Front. Math. China ›› 2020, Vol. 15 ›› Issue (5) : 1011 -1034. DOI: 10.1007/s11464-020-0864-7
RESEARCH ARTICLE
RESEARCH ARTICLE

Boundedness of multilinear singular integrals on central Morrey spaces with variable exponents

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Abstract

We prove the boundedness for a class of multi-sublinear singular integral operators on the product of central Morrey spaces with variable exponents. Based on this result, we obtain the boundedness for the multilinear singular integral operators and two kinds of multilinear singular integral commutators on the above spaces.

Keywords

Multilinear singular integral / variable exponent / central Morrey space

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Hongbin WANG, Jingshi XU, Jian TAN. Boundedness of multilinear singular integrals on central Morrey spaces with variable exponents. Front. Math. China, 2020, 15(5): 1011-1034 DOI:10.1007/s11464-020-0864-7

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References

[1]

Alvarez J, Lakey J, Guzmán-Partida M. Spaces of bounded-central mean oscillation, Morrey spaces, and λ-central Carleson measures. Collect Math, 2000, 51: 1–47

[2]

Chen Y, Levin S, Rao M. Variable exponent, linear growth functionals in image restoration. SIAM J Appl Math, 2006, 66: 1383–1406

[3]

Chuong N, Duong D, Hung H. Bounds for the weighted Hardy-Cesaro operator and its commutator on Morrey-Herz type spaces. Z Anal Anwend, 2016, 35: 489–504

[4]

Cruz-Uribe D, Fiorenza A. Variable Lebesgue Spaces: Foundations and Harmonic Analysis. Appl Numer Harmon Anal. Heidelberg: Springer, 2013

[5]

Cruz-Uribe D, Fiorenza A, Martell J M, Pérez C. The boundedness of classical operators on variable Lp spaces. Ann Acad Sci Fenn Math, 2006, 31: 239–264

[6]

Cruz-Uribe D, Fiorenza A, Neugebauer C. The maximal function on variable Lp spaces. Ann Acad Sci Fenn Math, 2003, 28: 223–238

[7]

Diening L, Harjulehto P, Hästö P, Růžička M. Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Math, Vol 2017. Heidelberg: Springer, 2011

[8]

Diening L, Růžička M. Calderón-Zygmund operators on generalized Lebesgue spaces L(·) and problems related to uid dynamics. J Reine Angew Math, 2003, 563: 197–220

[9]

Fu Z, Lin Y, Lu S. λ-central BMO estimates for commutators of singular integral operators with rough kernels. Acta Math Sin (Engl Ser), 2008, 24: 373–386

[10]

Fu Z, Lu S, Wang H, Wang L. Singular integral operators with rough kernels on central Morrey spaces with variable exponent. Ann Acad Sci Fenn Math, 2019, 44: 505–522

[11]

Grafakos L, Kalton N. Multilinear Calderón-Zygmund operators on Hardy spaces. Collect Math, 2001, 52: 169–179

[12]

Grafakos L, Torres R. Multilinear Calderón-Zygmund theory. Adv Math, 2002, 165: 124–164

[13]

Grafakos L, Torres R. Maximal operator and weighted norm inequalities for multilinear singular integrals. Indiana Univ Math J, 2002, 51: 1261–1276

[14]

Harjulehto P, Hästö P, U V, Nuortio M. Overview of differential equations with non-standard growth. Nonlinear Anal, 2010, 72: 4551–4574

[15]

Huang A, Xu J. Multilinear singular integrals and commutators in variable exponent Lebesgue spaces. Appl Math J Chinese Univ Ser B, 2010, 25: 69–77

[16]

Hussain A, Gao G. Multilinear singular integrals and commutators on Herz space with variable exponent. ISRN Math Anal, 2014, 2014: Article ID 626327 (10pp)

[17]

Izuki M. Boundedness of sublinear operators on Herz spaces with variable exponent and application to wavelet characterization. Anal Math, 2010, 36: 33–50

[18]

Kováčik O, Rákosník J. On spaces Lp(x) and Wk,p(x). Czechoslovak Math J, 1991, 41: 592–618

[19]

Lacey M, Thiele C. Lp estimates on the bilinear Hilbert transform for 2<p<∞ Ann of Math, 1997, 146: 693–724

[20]

Lacey M, Thiele C. On Calderón's conjecture. Ann of Math, 1999, 149: 475–496

[21]

Mizuta Y, Ohno T, Shimomura T. Boundedness of maximal operators and Sobolev's theorem for non-homogeneous central Morrey spaces of variable exponent. Hokkaido Math J, 2015, 44: 185–201

[22]

Pérez C, Trujillo-González R. Sharp weighted estimates for multilinear commutators. J Lond Math Soc, 2002, 65: 672–692

[23]

Růžička M. Electrorheological Fluids: Modeling and Mathematical Theory. Berlin: Springer, 2000

[24]

Sawano Y, Shimomura T. Boundedness of the generalized fractional integral operators on generalized Morrey spaces over metric measure spaces. Z Anal Anwend, 2017, 36: 159–190

[25]

Shi S, Lu S. Characterization of the central Campanato space via the commutator operator of Hardy type. J Math Anal Appl, 2015, 429: 713–732

[26]

Tan J, Liu Z, Zhao J. On multilinear commutators in variable Lebesgue spaces. J Math Inequal, 2017, 11: 715–734

[27]

Tang C, Wu Q, Xu J. Commutators of multilinear Calderón-Zygmund operator and BMO functions in Herz-Morrey spaces with variable exponents. J Funct Spaces, 2014, 2014: Article ID 162518 (12pp)

[28]

Tao X, Shi Y. Multilinear commutators of Calderón-Zygmund operator on λ-central Morrey spaces. Adv Math (China), 2011, 40: 47–59

[29]

Wang D, Liu Z, Zhou J, Teng Z. Central BMO spaces with variable exponent. Acta Math Sinica (Chin Ser), 2018, 61: 641–650 (in Chinese)

[30]

Wang H. The continuity of commutators on Herz-type Hardy spaces with variable exponent. Kyoto J Math, 2016, 56: 559–573

[31]

Wang H. Commutators of singular integral operator on Herz-type Hardy spaces with variable exponent. J Korean Math Soc, 2017, 54: 713–732

[32]

Wang H. Commutators of homogeneous fractional integrals on Herz-type Hardy spaces with variable exponent. J Contemp Math Anal, 2017, 52: 134–143

[33]

Wang H, Liao F. Boundedness of singular integral operators on Herz-Morrey spaces with variable exponent. Chin Ann Math Ser B, 2020, 41: 99–116

[34]

Wang H, Yan D. Commutators of Marcinkiewicz integrals with rough kernels on Herztype Hardy spaces with variable exponent. J Math Inequal, 2018, 12: 1173–1188

[35]

Wang L, Shu L. Multilinear commutators of singular integral operators in variable exponent Herz-type spaces. Bull Malays Math Sci Soc, 2019, 42: 1413{1432

[36]

Xu J. The boundedness of multilinear commutators of singular integrals on Lebesgue spaces with variable exponent. Czechoslovak Math J, 2007, 57: 13–27

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