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Generalized Hörmander conditions and weighted endpoint estimates


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Opened Access Generalized Hörmander conditions and weighted endpoint estimates

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Author: Lorente Domínguez. María
Martell Berrocal, José María
Pérez Moreno, Carlos
Riveros, María Silvina
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2009
Published in: Studia Mathematica, 195 (2), 157-192.
Document type: Article
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 Lp(v) to Lp,∞(u). One-sided singular integrals, as the differential transform operator, are under study. We also provide applications to Fourier multipliers and homogeneous singular integrals.
Cite: Lorente Domínguez. María, , Martell Berrocal, J.M., Pérez Moreno, C. y Riveros, M.S. (2009). Generalized Hörmander conditions and weighted endpoint estimates. Studia Mathematica, 195 (2), 157-192.
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DOI: 10.4064/sm195-2-5

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