On variable exponent Lebesgue spaces of entire analytic functions
The authors introduce the variable Lebesgue spaces of entire functions \(L^K_{p(\cdot)}\), where \(K\) is a compact subset of \({\mathbb R}^n\). They obtain a generalization of the maximal inequality of Jawerth and inequalities of Plancherel-Polya-Nikolskii type. They calculate the dual of the space \(L^K_{p(\cdot)}\) when the function \(\chi_K\) is an \(L_{p(\cdot)}\)-Fourier multiplier and give a number of consequences of this result (on sequence space representations). Finally, a Fourier multiplier theorem by Triebel is extended to the setting of variable exponent Lebesgue spaces.
\(L_p\)-spaces of entire analytic functions
scientific article; zbMATH DE number 6009597
scientific article