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

0433864 - MÚ 2015 RIV AM eng J - Journal Article
Fiorenza, A. - Gogatishvili, Amiran - Kopaliani, T.
Estimates for imaginary powers of the Laplace operator in variable Lebesgue spaces and applications.
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences. Roč. 49, č. 5 (2014), s. 232-240. ISSN 1068-3623. E-ISSN 1934-9416
R&D Projects: GA ČR GA13-14743S
Institutional support: RVO:67985840
Keywords : spherical maximal function * variable Lebesgue spaces * boundedness result
Subject RIV: BA - General Mathematics
Impact factor: 0.322, year: 2014
http://link.springer.com/article/10.3103/S1068362314050045

In this paper we study some estimates of norms in variable exponent Lebesgue spaces for singular integral operators that are imaginary powers of the Laplace operator in $R^n$. Using the Mellin transform argument, from these estimates we obtain the boundedness for a family of maximal operators in variable exponent Lebesgue spaces, which are closely related to the (weak) solution of the wave equation.
Permanent Link: http://hdl.handle.net/11104/0238043