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The Riesz-Herz equivalence for capacitary maximal functions
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
Barcelona University, Spain.
Linköping University.
2012 (English)In: Revista Matemática Complutense, ISSN 1139-1138, Vol. 25, no 1, 43-59 p.Article in journal (Refereed) Published
Abstract [en]

We prove a Riesz-Herz estimate for the maximal function associated toa capacity ConRn,MCf(x)=supQxC(Q)−1Q|f|, which extends the equivalence (Mf )∗(t)f∗∗(t) for the usual Hardy-Littlewood maximal function Mf. The proof is based on an extension of the Wiener-Stein estimates for the distribution function of the maximal function, obtained using a convenient family of dyadiccubes. As a byproduct we obtain a description of the norm of the interpolationspace (L1,L1,C)1/p,p,  where L1,C denotes the Morrey space based on a capacity.

Place, publisher, year, edition, pages
2012. Vol. 25, no 1, 43-59 p.
Keyword [en]
Maximal function, Capacity, Morrey space, Dyadic cubes, Interpolation spaces
National Category
Geometry
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-7631DOI: 10.1007/s13163-010-0057-0OAI: oai:DiVA.org:lnu-7631DiVA: diva2:344838
Available from: 2010-08-22 Created: 2010-08-22 Last updated: 2016-03-11Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • modern-language-association-8th-edition
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