On variable exponent Lebesgue spaces of entire analytic functions

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Abstract

In this article we introduce the variable Lebesgue spaces of entire analytic functions Lp()K. A maximal inequality of Jawerth is generalized to our context and inequalities of Plancherel–Polya–Nikolʼskij type are obtained. We calculate the dual of the space Lp()K when the function χK is an Lp()-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.

Keywords

Variable exponent
Lebesgue spaces
Lp-spaces of entire analytic functions
Maximal operators
Fourier multipliers

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Partially supported by MEC (Spain) Grant No. MTM2008-04594.