Generalized Hörmander conditions and weighted endpoint estimates

• Autorzy: María Lorente , José María Martell , Carlos Pérez , María Silvina Riveros
• Języki publikacji: EN

Abstrakty

EN

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 $L^{p,∞}(u)$. One-sided singular integrals, like the differential transform operator, are considered as well. We also provide applications to Fourier multipliers and homogeneous singular integrals.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 195
• Numer: 2
• Strony: 157-192

Daty

wydano

2009

Twórcy

autor

María Lorente

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos, s/n, 29071 Málaga, Spain

autor

José María Martell

• Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, C/ Serrano 121, 28006 Madrid, Spain

autor

Carlos Pérez

• Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41080 Sevilla, Spain

autor

María Silvina Riveros

• FaMAF, Universidad Nacional de Córdoba, CIEM (CONICET), 5000 Córdoba, Argentina

Identyfikatory

DOI

10.4064/sm195-2-5