广义加权极大Morrey空间中次线性算子的有界性质

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Zheng Qingyu, Zhang Lei, Shi Shaoguang. On Boundedness of Sublinear Operators on Generalized Weighted Grand Morrey Spaces[J].Acta mathematica scientia,Series A, 2015, 35(3): 503-514.

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[1] Morrey C. On the solutions of quasi-linear elliptic partial differential equations. Trans Amer Math Soc, 1938, 43: 126-166
[2] Duong X T, Xiao J, Yan L X. Old and new Morrey spaces with heat kernel bounds. J Fourier Anal Appl, 2007, 13: 87-111
[3] Yang D C, Yang D Y, Zhou Y. Localized Morrey-Campanato spaces on metric measure spaces and applications to Schrödinger operators. Nagoya Math J, 2010, 198: 77-119
[4] Yuan W, Sickel W, Yang D C. Morrey and Campanato Meet Besov, Lizorkin and Triebel, Lecture Notes in Mathematics, 2005. Berlin: Springer-Verlag, 2010
[5] Chiarenza F, Frasca M. Morrey spaces and Hardy-Littlewood maximal function. Rend Math Appl, 1987, 7: 273-279
[6] García-Cuerva J, Rubio de Francia J. Weighted Norm Inequalities and Related Topics. North-Holland Math Stud, Amsterdam: North-Holland, 1985
[7] Grafakos L. Classical and Modern Fourier Analysis. London: Prentice Hall, 2004
[8] Komori Y, Shirai S. Weighted Morrey spaces and a singular integral operator. Math Nachr, 2009, 282: 219-231
[9] Torchinsky A. Real Variable Methods in Harmonic Analysis. San Diego: Academic Press, 1986
[10] Meskhi A. Maximal functions, potentials and singular integrals in grand Morrey spaces. Complex Var Elliptic Equ, 2011, 56: 1003-1019
[11] Kokilashvili V. Boundedness criteria for singular integrals in weighted grand Lebesgue spaces. J Math Sci, 2010, 170: 20-23
[12] Greco L, Iwaniec T, Sbordone C. Inverting the p-harmonic operator. Manuscripta Math, 1997, 92: 249-258
[13] Fiorenza A. Duality and reflexivity in grand Lebesgue spaces. Collect Math, 2000, 51: 131-148
[14] Fiorenza A, Gupta B, Jain P. The maximal theorem in weighted grand Lebesgue spaces. Studia Math, 2008, 188: 123-133
[15] Iwaniec T, Sbordone C. On the integrability of the Jacobian under minimal hypotheses. Arch Rational Mech Anal, 1992, 119: 129-143
[16] Soria F, Weiss G. A remark on singular integrals and power weights. Indiana Univ Math J, 1994, 43: 187-204
[17] Bandaliev R. The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces. Czechoslovak Math J, 2010, 60: 327-337
[18] Fan D S, Lu S Z, Yang D C. Regularity in Morry spaces of strong solutions to nondivergence elliptic equations with VMO coefficients. Georgian Math J, 1998, 5: 425-440
[19] Chang C, Yang D C, Zhou Y. Boundedness of sublinear operator s on product Hardy spaces and its application. J Math Soc Japan, 2010, 62: 321-353
[20] Ding Y, Yang D C, Zhou Z. Boundedness of sublinear operators and commutators on L^p,w(Rⁿ). Yokohama Math J, 1998, 46: 15-27
[21] Lu S Z, Yang D C, Hu G E. Herz Type Spaces and Their Applications. Beijing: Science Press, 2008
[22] Lu S Z, Yang D C, Zhou Z. Sublinear operators with rough kernel on generalized Morrey spaces. Hokkaido Math J, 1998, 27: 219-232
[23] Shi S G, Fu Z W, Zhao F Y. Estimates for operators on weighted Morrey spaces and their applications to nondivergence elliptic equations. J Inequal Appl, 2013, 2013: 390
[24] Li X W, Yang D C. Boundedness of some sublinear operators on Herz spaces. Illinois J Math, 1996, 40: 484-501
[25] Ricci F, Stein E. Harmonic analysis on nilpotant groups and singular integrals I: Oscillatory Integrals. J Funct Anal, 1987, 73: 179-194.
[26] Hernandez E, Yang D C. Interpolation of Herz spaces and applications. Math Nachr, 1999, 205: 69-87
[27] Pérez C. Endpoint estimates for commutators of singular integral operators. J Func Anal, 1995, 128: 163-185
[28] Coifman R, Rochberg R, Weiss G. Factorization theorems for Hardy spaces in several variables. Ann Math, 1976, 103: 611-635
[29] Li P T, Peng L Z. L^P boundedness of commutators associtaed to Schrödinger operators Heisenberg group. Acta Mathematica Scientia, 2012, 32B(2): 568-578
[30] Lu G Z, Lu S Z, Yang D C. Singular integrals and commutators on homogeneous groups. Anal Math, 2002, 28: 103-134
[31] 乔丹, 杨美金, 陈建仁. 极大高阶交换子的端点估计. 数学物理学报, 2012, 32A(2): 320-335
[32] Segovia C, Tottra J. Weighted inequalities for commutators of fractional and singular integrals. Publ Math, 1991, 35: 209-235
[33] Muckenhoupt B, Wheeden R. Weighted bounded mean oscillation and the Hilbert transform. Studia Math, 1976, 54: 221-237

On Boundedness of Sublinear Operators on Generalized Weighted Grand Morrey Spaces

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