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Weighted Stepanov-Like Pseudo-Almost Periodic Functions in Lebesgue Space with Variable Exponents $L^p(x)$

Volume 15, Number 2 (2013), 56 - 75

Weighted Stepanov-Like Pseudo-Almost Periodic Functions in Lebesgue Space with Variable Exponents $L^{p(x)}$

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Abstract

In this paper we introduce and study a new class of functions called $S^{p,q(x)}$-pseudoalmost periodic (or weighted Stepanov-like pseudo-almost periodic functions with variable exponents), which generalizes the class of weighted Stepanov-like pseudoalmost periodic functions. Basic properties of these new spaces are established. The existence of weighted pseudo-almost periodic solutions to some first-order differential equations with $S^{p,q(x)}$-pseudo-almost periodic coefficients will also be studied.