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arXiv · 1304.6853

Some estimates for imaginary powers of the Laplace operator in variable Lebesgue spaces and applications

Alberto Fiorenza·Amiran Gogatishvili·Tengiz Kopaliani
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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 $\R^n$. 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

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Alberto Fiorenza, Amiran Gogatishvili, Tengiz Kopaliani. 2013-12-27. Some estimates for imaginary powers of the Laplace operator in variable Lebesgue spaces and applications. https://arxiv.org/abs/1304.6853

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