Maximal functions, Riesz potentials and Sobolev’s inequality in generalized Lebesgue spaces. (English) Zbl 1125.31001

Aikawa, Hiroaki (ed.) et al., Potential theory in Matsue. Selected papers of the international workshop on potential theory, Matsue, Japan, August 23–28, 2004. Tokyo: Mathematical Society of Japan (ISBN 4-931469-33-7/hbk). Advanced Studies in Pure Mathematics 44, 255-281 (2006).
The aim of this paper is to deal with the boundedness of maximal functions in Lebesgue spaces \(L^{p(\cdot)}\) with variable exponent \(p(\cdot)\). As an application of the boundedness of maximal functions the authors show Sobolev’s inequality for Riesz potentials with variable exponent.
For the entire collection see [Zbl 1102.31001].


31B15 Potentials and capacities, extremal length and related notions in higher dimensions
42B25 Maximal functions, Littlewood-Paley theory
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)