Some estimates for imaginary powers of the Laplace operator in variable Lebesgue spaces and applications
Analysis of PDEs
2013-12-30 v2 Functional Analysis
Abstract
In this paper we study some estimates of norms in variable exponent Lebesgue spaces for a singular integral operators that are imaginary powers of the Laplace operator in . Using Mellin transform argument, from this estimates we obtain boundedness for a family of maximal operators in variable exponent Lebesgue spaces, which are closely related to the (weak) solution of the wave equation.42B25, 42B20, 46E30, 44A10, 42B10, 35L05
Keywords
Cite
@article{arxiv.1304.6853,
title = {Some estimates for imaginary powers of the Laplace operator in variable Lebesgue spaces and applications},
author = {Alberto Fiorenza and Amiran Gogatishvili and Tengiz Kopaliani},
journal= {arXiv preprint arXiv:1304.6853},
year = {2013}
}