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Distribution and Rearranement Estimates of the Maximal Functions and Interpolation
Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM. (mathematics)
Department of Mathematics, Yaroslavl' State University, Russia.
Department of Mathematics, Luleå University of Technology, Sweden.
Department of Mathematics, Luleå University of Technology, Sweden.
1997 (English)In: Studia Mathematica, ISSN 0039-3223, Vol. 124, no 2, 107-132 p.Article in journal (Refereed) Published
Abstract [en]

There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition. Analogous methods allow us to obtain K-functional formulas in terms of the maximal function for couples of weighted $L_p$-spaces.

Place, publisher, year, edition, pages
1997. Vol. 124, no 2, 107-132 p.
Keyword [en]
Real interpolation, maximal function, distribution
National Category
Mathematical Analysis
Research subject
Natural Science, Mathematics
URN: urn:nbn:se:liu:diva-106170OAI: diva2:714482
Available from: 2010-08-22 Created: 2014-04-28 Last updated: 2014-04-28Bibliographically approved

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Asekritova, Irina
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