Local Hardy-Littlewood maximal operator in variable Lebesgue spaces

Author: Tengiz Kopaliani
Co-authors: A. Gogatishvili, A. Danelia
Keywords: local Muckenhoupt classes, Littlewood-Paley theory, square function
Annotation:

We investigate the class of exponents for which the local Hardy-Littlewood maximal operator is bounded in variable exponent Lebesgue spaces. Littlewood-Paley square function characterization of this spaces are also obtained.