Local Hardy--Littlewood maximal operator in variable Lebesgue spaces

A. Danelia; A. Gogatishvili; T. Kopaliani

doi:10.15352/bjma/1396640066

2014 Local Hardy--Littlewood maximal operator in variable Lebesgue spaces

A. Danelia, A. Gogatishvili, T. Kopaliani

Banach J. Math. Anal. 8(2): 229-244 (2014). DOI: 10.15352/bjma/1396640066

Abstract

We investigate the class $\mathcal{B}^{loc}(\mathbb{R}^{n})$ of exponents $p(\cdot)$ for which the local Hardy-Littlewood maximal operator is bounded in variable exponent Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^{n})$. Littlewood-Paley square function characterization of $L^{p(\cdot)}(\mathbb{R}^{n})$ spaces with the above class of exponent are also obtained.

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A. Danelia, A. Gogatishvili, and T. Kopaliani "Local Hardy--Littlewood maximal operator in variable Lebesgue spaces," Banach Journal of Mathematical Analysis 8(2), 229-244, (2014). https://doi.org/10.15352/bjma/1396640066

Published: 2014

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