Geodesic
Distribution and rearrangement estimates of the maximal function and interpolation
Studia Mathematica, Tome 124 (1997) no. 2, pp. 107-132

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-124-2-107-132
Keywords: maximal functions, weights, weak type estimate, rearrangement, distribution functioni, inequalities, interpolation, K-functional, weighted spaces

Irina U. Asekritova 1 ;  1 ;  1 ;  1

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Irina U.  Asekritova;  ;  ;  . Distribution and rearrangement estimates of the maximal function and interpolation. Studia Mathematica, Tome 124 (1997) no. 2, pp. 107-132. doi: 10.4064/sm-124-2-107-132

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