A boundedness criterion via atoms for linear operators in Hardy spaces

DOI10.1007/s00365-008-9015-1zbMath1283.42029OpenAlexW1996897278MaRDI QIDQ2272170

Publication date: 6 August 2009

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-008-9015-1

zbMATH Keywords

Hardy space atom quasi-Banach space linear operator boundedness criterion Caldéron reproducing formula

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) (H^p)-spaces (42B30)

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Cites Work