Differential properties of bases and halo problem for rearrangement-invariant spaces

DOI10.1007/BF02106832zbMath0877.46017MaRDI QIDQ1920859

E. I. Berezhnoi

Publication date: 8 December 1997

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

boundednessmaximal operatorsMarcinkiewicz spacedifferentiation basesrearrangement-invariant spacescovering propertiesdilatation operatordifferentiation properties of basesLorentz, Marcinkiewicz, and Orlicz spaces

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) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

Cites Work

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• Note on differentiation of integrals and the halo conjecture
• A negative result in differentiation theory
• On the differentiation of integrals of functions from Lφ(L)
• On the differentiation of integrals of functions from Orlicz classes
• Note on the differentiability of multiple integrals

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