Geodesic
Generalized Hörmander conditions and weighted endpoint estimates
María Lorente 1   ; José María Martell 2   ; Carlos Pérez 3   ; María Silvina Riveros 4
1 Departamento de Análisis Matemático Facultad de Ciencias Universidad de Málaga Campus de Teatinos, s//n 29071 Málaga, Spain
2 Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM Consejo Superior de Investigaciones Científicas C/ Serrano 121 28006 Madrid, Spain
3 Departamento de Análisis Matemático Facultad de Matemáticas Universidad de Sevilla 41080 Sevilla, Spain
4 FaMAF Universidad Nacional de Córdoba CIEM (CONICET) 5000 Córdoba, Argentina
Studia Mathematica, Tome 195 (2009) no. 2, pp. 157-192 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm195-2-5
Keywords: consider two weight estimates singular integral operators their commutators bounded mean oscillation functions rmander type conditions scale orlicz spaces assumed kernels prove weighted weak type estimates pairs weights where arbitrary nonnegative function maximal operator depending smoothness kernel obtain sufficient conditions pair weights operators bounded infty one sided singular integrals differential transform operator considered provide applications fourier multipliers homogeneous singular integrals

María Lorente  1   ; José María Martell  2   ; Carlos Pérez  3   ; María Silvina Riveros  4

1 Departamento de Análisis Matemático Facultad de Ciencias Universidad de Málaga Campus de Teatinos, s//n 29071 Málaga, Spain
2 Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM Consejo Superior de Investigaciones Científicas C/ Serrano 121 28006 Madrid, Spain
3 Departamento de Análisis Matemático Facultad de Matemáticas Universidad de Sevilla 41080 Sevilla, Spain
4 FaMAF Universidad Nacional de Córdoba CIEM (CONICET) 5000 Córdoba, Argentina 
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     title = {Generalized {H\"ormander} conditions and
 weighted endpoint estimates},
     journal = {Studia Mathematica},
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 weighted endpoint estimates
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 weighted endpoint estimates
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María Lorente; José María Martell; Carlos Pérez; María Silvina Riveros. Generalized Hörmander conditions and
 weighted endpoint estimates. Studia Mathematica, Tome 195 (2009) no. 2, pp. 157-192. doi: 10.4064/sm195-2-5

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