Abstract
Applying the new class of multiple weights functions and new sharp maximal functions, we obtain the pointwise estimates, strong type and weak end-point estmates for certain classes of multilinear operators and their iterated commutators with new BMO functions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bényi, Á., Torres, R.: Symbolic calculus and the transposes of bilinear pseudodifferential operators. Comm. Par. Diff. Eq 28, 1161–1181 (2003)
Bui, T.A.: New class of multiple weights and new weighted inequalities for multilinear operators, to appear in Forum Math (arXiv:1203.2797(2012))
Bongioanni, B., Haboure, E., Salinas, O.: Commutators of Riesz transforms related to Schrödinger operators. J. Fourier Anal. Appl 17, 115–134 (2011)
Bongioanni, B., Haboure, E., Salinas, O.: Classes of weights related to Schrödinger operators. J. Math. Anal. Appl 373, 563–579 (2011)
Coifman, R., Rochberg, R., Weiss, G.: Factorization theorems for Hardy spaces in several variables. Ann. of Math. 103, 611–635 (1976)
García-Cuerva, J., Rubio de Francia, J.: Weighted Norm Inequalities and Related Topics. Amsterdam- New York, North-Holland (1985)
Grafakos, L., Torres, R.H.: Multilinear Calderón-Zygmund theory. Adv. Math 165(1), 124–164 (2002)
Lerner, A.K., Ombrosi, S., Pérez, C., Torres, R.H., Trujillo-González, R.: New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory. Adv. Math 220(4), 1222–1264 (2009)
Pérez, C.: Endpoint estimates for commutators of singular integrals. J. Funct Anal 128, 163–185 (1995)
Pérez, C., Pradolini, G.: Sharp weighted endpoint estimates for commutators of singular integral operators. Michigan Math. J 49, 23–37 (2001)
Pérez, C., Pradolini, G., Torres, R., Trujillo-Gonzalez, R.: End-point estimates for iterated commutators of multilinear singular integrals. Bull. London Math. Soc 46, 26–42 (2014)
Pérez, C., Torres, R.: Sharp maximal function estimates for multilinear singular integrals. Contemp. Math. 320, 323–331 (2003)
Tang, L.: Weighted norm inequalities for pseudo-differential operators with smooth symbols and their commutators. J. Funct. Anal 262, 1603–1629 (2012)
Tang, L., from, Extrapolation: \(A^{\rho ,\infty }_{\infty }\), Vector-valued inequalities and applications in Schrödinger settings. Ark. Mat 52, 175–202 (2014)
Wilson, M.: Weighted Littlewood-Paley Theory and Exponential-Square Integrability, Lecture Notes in Math, vol. 1924. Springer, Berlin (2008)
Rao, M.M., Ren, Z.D.: Theory of Orlicz Spaces. Marcel Dekker, New York (1991)
Author information
Authors and Affiliations
Corresponding author
Additional information
The research was supported by the NNSF (11271024) of China.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Pan, G., Tang, L. New Weighted Norm Inequalities for Certain Classes of Multilinear Operators and their Iterated Commutators. Potential Anal 43, 371–398 (2015). https://doi.org/10.1007/s11118-015-9477-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11118-015-9477-2