On variable exponent Lebesgue spaces of entire analytic functions

Abstract

In this article we introduce the variable Lebesgue spaces of entire analytic functions Lp({dot operator})K. A maximal inequality of Jawerth is generalized to our context and inequalities of Plancherel-Polya-Nikol'skij type are obtained. We calculate the dual of the space Lp({dot operator})K when the function ¿ K is an L p({dot operator})-Fourier multiplier and a number of consequences of this result (on sequence space representations) is given. Finally, a Fourier multiplier theorem by Triebel is extended to the setting of the variable Lebesgue spaces. © 2011 Elsevier Inc.