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.
Citation
A. Danelia. A. Gogatishvili. T. Kopaliani. "Local Hardy--Littlewood maximal operator in variable Lebesgue spaces." Banach J. Math. Anal. 8 (2) 229 - 244, 2014. https://doi.org/10.15352/bjma/1396640066
Information