Boundedness of the Maximal Operator in the Banach Function Spaces

Author: Daviti Adamadze
Co-authors: Tengiz Kopaliani, Lars Diening
Keywords: Maximal Operator. Variable Lebesgue Space.
Annotation:

In the present project, we investigate the boundedness of the Hardy-Littlewood maximal operator in limiting case of the exponent, in the variable Lebesgue space. The obtained result is a generalization of Lerner’s theorem about the boundedness of the Hardy-Littlewood maximal operator in terms of the Muckenhoupt-type condition.