Weighted Boundedness of Maximal Functions and Fractional Bergman Operators

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Date

2018-04

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Journal of Geometric Analysis

Abstract

The aim of this paper is to study two-weight norm inequalities for fractional maximal functions and fractional Bergman operator defined on the upper-half space. Namely, we characterize those pairs of weights for which these maximal operators satisfy strong and weak type inequalities. Our characterizations are in terms of Sawyer and B\'ekoll\'e-Bonami type conditions. We also obtain a $\Phi$-bump characterization for these maximal functions, where $\Phi$ is a Orlicz function. As a consequence, we obtain two-weight norm inequalities for fractional Bergman operators. Finally, we provide some sharp weighted inequalities for the fractional maximal functions.

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Keywords

Bergman operator, Békollè–Bonami weight, Carleson-type embedding, Dyadic grid, Maximal function, Upper-half plane

Citation

Sehba, B.F. J Geom Anal (2018) 28: 1635. https://doi.org/10.1007/s12220-017-9881-5

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