Operators of Harmonic Analysis in Variable Exponent Lebesgue Spaces. Two-Weight Estimates

Details Operators of Harmonic Analysis in Variable Exponent Lebesgue Spaces. Two-Weight Estimates Operators of Harmonic Analysis in Variable Exponent Lebesgue Spaces. Two-Weight Estimates

2010-07-08

arxiv.org/abs/1007.1351v1

Mathematics

Functional Analysis

24 pages

Scientific paper

In the paper two-weighted norm estimates with general weights for Hardy-type transforms, maximal functions, potentials and Calder\'on-Zygmund singular integrals in variable exponent Lebesgue spaces defined on quasimetric measure spaces $(X, d, \mu)$ are established. In particular, we derive integral-type easily verifiable sufficient conditions governing two-weight inequalities for these operators. If exponents of Lebesgue spaces are constants, then most of the derived conditions are simultaneously necessary and sufficient for appropriate inequalities. Examples of weights governing the boundedness of maximal, potential and singular operators in weighted variable exponent Lebesgue spaces are given.

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