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Wavelets and modular inequalities in variable \(L^{p}\) spaces. (English) Zbl 1152.42014

Summary: The aim of this paper is to characterize variable \(L^p\) spaces \(L^{p(\cdot)} (\mathbb{R}^n)\) using wavelets with proper smoothness and decay. We obtain conditions for the wavelet characterizations of \(L^{p(\cdot)}(\mathbb{R}^n)\) with respect to the norm estimates and modular inequalities.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
42B35 Function spaces arising in harmonic analysis
42C15 General harmonic expansions, frames
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
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