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Generalized Hörmander conditions and weighted endpoint estimates

Volume 195 / 2009

María Lorente, José María Martell, Carlos Pérez, María Silvina Riveros Studia Mathematica 195 (2009), 157-192 MSC: 42B20, 42B25. DOI: 10.4064/sm195-2-5

Abstract

We consider two-weight estimates for singular integral operators and their commutators with bounded mean oscillation functions. Hörmander type conditions in the scale of Orlicz spaces are assumed on the kernels. We prove weighted weak-type estimates for pairs of weights $(u, Su)$ where $u$ is an arbitrary nonnegative function and $S$ is a maximal operator depending on the smoothness of the kernel. We also obtain sufficient conditions on a pair of weights $(u,v)$ for the operators to be bounded from $L^p(v)$ to $L^{p,\infty }(u)$. One-sided singular integrals, like the differential transform operator, are considered as well. We also provide applications to Fourier multipliers and homogeneous singular integrals.

Authors

  • María LorenteDepartamento de Análisis Matemático
    Facultad de Ciencias
    Universidad de Málaga
    Campus de Teatinos, s//n
    29071 Málaga, Spain
    e-mail
  • José María MartellInstituto de Ciencias Matemáticas
    CSIC-UAM-UC3M-UCM
    Consejo Superior de Investigaciones Científicas
    C/ Serrano 121
    28006 Madrid, Spain
    e-mail
  • Carlos PérezDepartamento de Análisis Matemático
    Facultad de Matemáticas
    Universidad de Sevilla
    41080 Sevilla, Spain
    e-mail
  • María Silvina RiverosFaMAF
    Universidad Nacional de Córdoba
    CIEM (CONICET)
    5000 Córdoba, Argentina
    e-mail

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