- Tytuł:
- Distribution and rearrangement estimates of the maximal function and interpolation
- Autorzy:
-
U. Asekritova, Irina
Krugljak, Natan
Maligranda, Lech
Persson, Lars-Erik - Powiązania:
- https://bibliotekanauki.pl/articles/1219812.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
maximal functions
weights
weak type estimate
rearrangement
distribution functioni
inequalities
interpolation
K-functional
weighted spaces - Opis:
- 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.
- Źródło:
-
Studia Mathematica; 1997, 124, 2; 107-132
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł