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Matematicheskie Zametki, 2007, Volume 81, Issue 4, Pages 483–489
DOI: https://doi.org/10.4213/mzm3691 (Mi mzm3691) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the Normability of Marcinkiewicz Classes

S. V. Astashkin

Samara State University
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DOI: https://doi.org/10.4213/mzm3691
Abstract: We obtain simple necessary and sufficient conditions for the normability of Marcinkiewicz classes, which play an important role in various problems of analysis. These conditions are stated in terms of dilation exponents of the function generating the given class as well as in terms of interpolation for operators bounded in the couple $(L_1,L_\infty)$.
Keywords: Marcinkiewicz class, normability, generating function, interpolation, dilation exponent, quasinorm, Hardy–Littlewood operator, symmetric Banach space.
Received: 10.10.2005
Revised: 06.06.2006
English version:
Mathematical Notes, 2007, Volume 81, Issue 4, Pages 429–434
DOI: https://doi.org/10.1134/S0001434607030182
Bibliographic databases:
UDC: 517.982.27
Language: Russian
Citation: S. V. Astashkin, “On the Normability of Marcinkiewicz Classes”, Mat. Zametki, 81:4 (2007), 483–489; Math. Notes, 81:4 (2007), 429–434
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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