On variable exponent Lebesgue spaces of entire analytic functions

Autores UPV
Revista Journal of Mathematical Analysis and Applications


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.