English

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 Rn\R^n. 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}
}