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Distribution and rearrangement estimates of the maximal function and interpolation

100%

U. Asekritova I., Krugljak N. Y., Maligranda L., Persson L.-E.

Studia Mathematica

1997

tom 124

nr 2

107-132

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.

Ograniczanie wyników

1 Studia Mathematica

1 Krugljak N. Y.

1 Maligranda L.

1 Persson L.-E.

1 U. Asekritova I.

1 1997

Wyniki wyszukiwania

Distribution and rearrangement estimates of the maximal function and interpolation