S. V. Astashkin, “On the Normability of Marcinkiewicz Classes”, Mat. Zametki, 2007, Volume 81, Issue 4,Pages <nobr>483

This article is cited in 2 papers

On the Normability of Marcinkiewicz Classes

S. V. Astashkin

Samara State University

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.

UDC: 517.982.27

Received: 10.10.2005
Revised: 06.06.2006

DOI: 10.4213/mzm3691