Distribution and Rearranement Estimates of the Maximal Functions and Interpolation
1997 (English)In: Studia Mathematica, ISSN 0039-3223, Vol. 124, no 2, 107-132 p.Article in journal (Refereed) Published
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.
Real interpolation, maximal function, distribution
Research subject Natural Science, Mathematics
IdentifiersURN: urn:nbn:se:liu:diva-106170OAI: oai:DiVA.org:liu-106170DiVA: diva2:714482