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Distribution and Re...
Distribution and Rearranement Estimates of the Maximal Functions and Interpolation
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- Asekritova, Irina (author)
- Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM,mathematics
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- Kruglyak, Natan (author)
- Department of Mathematics, Yaroslavl' State University, Russia
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- Maligranda, Lech (author)
- Department of Mathematics, Luleå University of Technology, Sweden
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- Persson, Lars-Erik (author)
- Department of Mathematics, Luleå University of Technology, Sweden
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(creator_code:org_t)
- 1997
- 1997
- English.
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In: Studia Mathematica. - 0039-3223 .- 1730-6337. ; 124:2, s. 107-132
- Related links:
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https://urn.kb.se/re...
Abstract
Subject headings
Close
- 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- Real interpolation
- maximal function
- distribution
- Mathematical analysis
- Analys
- Matematik
- Mathematics
Publication and Content Type
- ref (subject category)
- art (subject category)
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