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

0433864 - MÚ 2015 RIV AM eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR GA13-14743S
Institucionální podpora: RVO:67985840
Klíčová slova: spherical maximal function * variable Lebesgue spaces * boundedness result
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.322, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0238043