Singular and fractional integral operators on weighted local Morrey spaces

2021/10/27 by Duoandikoetxea, Javier, Rosenthal, Marcel
#42B20 #42B35 #46E30 #47G40 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2110.14259

Abstract

We obtain a characterization of the weighted inequalities for the Riesz transforms on weighted local Morrey spaces. The condition is sufficient for the boundedness on the same spaces of all Calderón-Zygmund operators suitably defined on the functions of the space. In the case of the fractional maximal operator and the fractional integral we obtain a characterization valid for exponents satisfying the Sobolev relation. For power weights we get sharp results in a larger range of exponents for the usual versions of weighted Morrey spaces.

Related

• Multilinear singular and fractional integral operators on weighted Morrey spaces
• Fractional operators on weighted Morrey spaces
• Boundedness of the Hardy-Littlewood Maximal Operator, Fractional Integral Operators, and Calderon-Zygmund Operators on Generalized Weighted Morrey Spaces
• Morrey Spaces and Fractional Integral Operators
• The singular integral operator and its commutator on weighted Morrey spaces