Izuki, Mitsuo Wavelets and modular inequalities in variable \(L^{p}\) spaces. (English) Zbl 1152.42014 Georgian Math. J. 15, No. 2, 281-293 (2008). 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. Cited in 1 ReviewCited in 10 Documents 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 Keywords:wavelet; unconditional basis; variable \(L^p\)-space PDFBibTeX XMLCite \textit{M. Izuki}, Georgian Math. J. 15, No. 2, 281--293 (2008; Zbl 1152.42014)