Local Hardy-Littlewood maximal opeator in variable Lebesgue spaces

Abstract

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

15 pages