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The Riesz-Herz equivalence for capacitary maximal functions
Linnaeus University.
University of Barcelona.
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
2012 (English)In: REVISTA MATEMATICA 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 to a capacity C on a"e (n) , M (C) f(x)=sup (Qa andlt; x) C(Q)(-1)a andlt;andlt; (Q) |f|, which extends the equivalence (Mf)(au)(t)a parts per thousand integral f (auau)(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 dyadic cubes. As a byproduct we obtain a description of the norm of the interpolation space (L(1), L(1,C))(1/p,p), where L(1), C denotes the Morrey space based on a capacity.

Place, publisher, year, edition, pages
Springer Verlag (Germany) , 2012. Vol. 25, no 1, 43-59 p.
Keyword [en]
Maximal function, Capacity, Morrey space, Dyadic cubes, Interpolation spaces
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-74850DOI: 10.1007/s13163-010-0057-0ISI: 000299056200004OAI: diva2:496576
Funding Agencies|DGICYT|MTM2007-60500|Available from: 2012-02-10 Created: 2012-02-10 Last updated: 2012-02-10

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Kruglyak, Natan
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Department of MathematicsThe Institute of Technology
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ReferencesLink to record
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