Atomic decompositions of localized Hardy spaces with variable exponents and applications

DOI10.1007/s12220-018-0019-1zbMath1407.42012OpenAlexW2794698712MaRDI QIDQ1725899

Jian Tan

Publication date: 15 February 2019

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-018-0019-1

zbMATH Keywords

atomic decompositionpseudo-differential operatorvariable exponent analysisLittlewood-Paley-Stein square functionlocalized Hardy space

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Maximal functions, Littlewood-Paley theory (42B25) Function spaces arising in harmonic analysis (42B35) (H^p)-spaces (42B30)

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Cites Work

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• An example of a space of \(L^{p(x)}\) on which the Hardy-Littlewood maximal operator is not bounded
• Atomic decompositions of weighted Hardy spaces with variable exponents
• Atomic decomposition of variable Hardy spaces via Littlewood-Paley-Stein theory
• A characterization of $H^{p}(R^{n})$ in terms of atoms
• Littlewood-Paley theory on spaces of homogeneous type and the classical function spaces
• A real variable characterization of $H^{p}$
• Variable Hardy Spaces
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