New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory

Advances in Mathematics - Tập 220 - Trang 1222-1264 - 2009
Andrei K. Lerner1, Sheldy Ombrosi2, Carlos Pérez1, Rodolfo H. Torres3, Rodrigo Trujillo-González4
1Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41080 , Sevilla, Spain
2Departamento de Matemática, Universidad Nacional del Sur, Bahía Blanca 8000, Argentina
3Department of Mathematics, University of Kansas, 405 Snow Hall 1460 Jayhawk Blvd, Lawrence, Kansas 66045-7523, USA
4Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, S.C. de Tenerife, Spain

Tài liệu tham khảo

Alvarez, 1994, Estimates with A∞ weights for various singular integral operators, Boll. Unione Mat. Ital. Sez. A (7), 8, 123 Bennett, 1988, Interpolation of Operators, vol. 129 Calderón, 1952, On the existence of certain singular integrals, Acta Math., 88, 85, 10.1007/BF02392130 Chiarenza, 1991, Interior W2,p estimates for non-divergence elliptic equations with discontinuous coefficients, Ric. Mat., 40, 149 Chiarenza, 1993, W2,p-solvability of the Dirichlet problem for non-divergence elliptic equations with VMO coefficients, Trans. Amer. Math. Soc., 334, 841 Christ, 1990, Lectures on Singular Integral Operators, vol. 77 Christ, 1983, A note on weighted norm inequalities for the Hardy–Littlewood maximal operator, Proc. Amer. Math. Soc., 87, 447, 10.1090/S0002-9939-1983-0684636-9 Christ, 1987, Polynomial growth estimates for multilinear singular integral operators, Acta Math., 159, 51, 10.1007/BF02392554 Coifman, 1974, Weighted norm inequalities for maximal functions and singular integrals, Studia Math., 51, 241, 10.4064/sm-51-3-241-250 Coifman, 1975, On commutators of singular integrals and bilinear singular integrals, Trans. Amer. Math. Soc., 212, 315, 10.1090/S0002-9947-1975-0380244-8 Coifman, 1978, Commutateurs d'intégrales singulières et opérateurs multilinéaires, Ann. Inst. Fourier (Grenoble), 28, 177, 10.5802/aif.708 Coifman, 1986, Nonlinear harmonic analysis, operator theory and P.D.E., vol. 112, 3 Coifman, 1976, Factorization theorems for Hardy spaces in several variables, Ann. of Math., 103, 611, 10.2307/1970954 Cruz-Uribe, 2005, Weighted weak-type inequalities and a conjecture of Sawyer, Int. Math. Res. Not., 30, 1849, 10.1155/IMRN.2005.1849 Cruz-Uribe, 1995, The structure of the reverse Hölder classes, Trans. Amer. Math. Soc., 347, 2941 Curbera, 2006, Extrapolation with weights to rearrangement invariant function spaces and modular inequalities, with applications to singular integrals, Adv. Math., 203, 256, 10.1016/j.aim.2005.04.009 Di Fazio, 1993, Interior estimates in Morrey spaces for strong solutions to nondivergence form equations with discontinuous coefficients, J. Funct. Anal., 112, 241, 10.1006/jfan.1993.1032 Fefferman, 1971, Some maximal inequalities, Amer. J. Math., 93, 107, 10.2307/2373450 Fefferman, 1972, Hp spaces of several variables, Acta Math., 129, 137, 10.1007/BF02392215 Fefferman, 1999, Multiparameter Calderón–Zygmund theory, 207 Ferguson, 2002, A characterization of product BMO by commutators, Acta Math., 189, 143, 10.1007/BF02392840 García-Cuerva, 1985 Grafakos, 2004 Grafakos, 2004, Extrapolation of weighted norm inequalities for multivariable operators and applications, J. Geom. Anal., 14, 19, 10.1007/BF02921864 Grafakos, 2002, Multilinear Calderón–Zygmund theory, Adv. Math., 165, 124, 10.1006/aima.2001.2028 Grafakos, 2002, Maximal operator and weighted norm inequalities for multilinear singular integrals, Indiana Univ. Math. J., 51, 1261, 10.1512/iumj.2002.51.2114 Grafakos, 2002, On multilinear singular integrals of Calderón–Zygmund type, 57 Iwaniec, 1994, Weak minima of variational integrals, J. Reine Angew. Math., 454, 143 Janson, 1978, Mean oscillation and commutators of singular integral operators, Ark. Mat., 16, 263, 10.1007/BF02386000 Jawerth, 1985, Local sharp maximal functions, J. Approx. Theory, 43, 231, 10.1016/0021-9045(85)90102-9 John, 1961, On functions of bounded mean oscillation, Comm. Pure Appl. Math., 14, 415, 10.1002/cpa.3160140317 Journé, 1983, Calderón–Zygmund Operators, Pseudo-differential Operators and the Cauchy Integral of Calderón, vol. 994 Kenig, 1999, Multilinear estimates and fractional integration, Math. Res. Lett., 6, 1, 10.4310/MRL.1999.v6.n1.a1 M. Lacey, S. Petermichl, J. Pipher, B. Wick, Multiparameter Riesz commutators, Amer. J. Math., in press Lacey, 1997, Lp estimates on the bilinear Hilbert transform for 2<p<∞, Ann. of Math. (2), 146, 693, 10.2307/2952458 Lacey, 1999, On Calderón's conjecture, Ann. of Math. (2), 149, 475, 10.2307/120971 Lerner, 2004, On some pointwise inequalities, J. Math. Anal. Appl., 289, 248, 10.1016/j.jmaa.2003.09.051 Lerner, 2008, An elementary approach to several results on the Hardy–Littlewood maximal operator, Proc. Amer. Math. Soc., 136, 2829, 10.1090/S0002-9939-08-09318-0 Martín-Reyes, 1995, On the one-sided Hardy–Littlewood maximal function in the real line and in dimensions greater than one, 237 Muckenhoupt, 1972, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc., 165, 207, 10.1090/S0002-9947-1972-0293384-6 Pérez, 1994, Weighted norm inequalities for singular integral operators, J. London Math. Soc., 49, 296, 10.1112/jlms/49.2.296 Pérez, 1995, Endpoint estimates for commutators of singular integral operators, J. Funct. Anal., 128, 163, 10.1006/jfan.1995.1027 Pérez, 1995, On sufficient conditions for the boundedness of the Hardy–Littlewood maximal operator between weighted Lp-spaces with different weights, Proc. London Math. Soc. (3), 71, 135, 10.1112/plms/s3-71.1.135 Pérez, 2001, Sharp weighted endpoint estimates for commutators of singular integral operators, Michigan Math. J., 49, 23 Pérez, 2003, Sharp maximal function estimates for multilinear singular integrals, vol. 320, 323 Rao, 1991 Stein, 1969, Note on the class LlogL, Studia Math., 32, 305, 10.4064/sm-32-3-305-310 Stein, 1998, Singular integrals: The roles of Calderón and Zygmund, Notices Amer. Math. Soc., 45, 1130 Volberg, 2003, Calderón–Zygmund Capacities and Operators on Nonhomogeneous Spaces, vol. 100 Wilson, 2008, Weighted Littlewood–Paley Theory and Exponential-Square Integrability, vol. 1924