Distribution and rearrangement estimates of the maximal function and interpolation
作者： Lech Maligranda , Natan Ya. Krugljak , Irina U. Asekritova , Lars-Erik Persson
DOI:
关键词:
摘要: There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for distribution rearrangement of maximal function due to Riesz, Wiener, Herz Stein valid. As consequence, we obtain equivalence Riesz Wiener inequalities seems be new even Lebesgue measure. Our main tools averaging f** modified version Calderon-Zygmund decomposition. Analogous methods allow us K-functional formulas in terms couples weighted $L_p$-spaces.
参考文章(11)
A. P. Calderon, A. Zygmund, On the existence of certain singular integrals Acta Mathematica. ,vol. 88, pp. 85- 139 ,(1952) , 10.1007/BF02392130
Frédéric Riesz, Sur un Théorème de Maximum de Mm. Hardy et Littlewood Journal of the London Mathematical Society. ,vol. s1-7, pp. 10- 13 ,(1932) , 10.1112/JLMS/S1-7.1.10
Norbert Wiener, The ergodic theorem Duke Mathematical Journal. ,vol. 5, pp. 1- 18 ,(1939) , 10.1215/S0012-7094-39-00501-6
G. H. Hardy, J. E. Littlewood, A maximal theorem with function-theoretic applications Acta Mathematica. ,vol. 54, pp. 81- 116 ,(1930) , 10.1007/BF02547518
Peter Sjogren, A Remark on the Maximal Function for Measures in R n American Journal of Mathematics. ,vol. 105, pp. 1231- ,(1983) , 10.2307/2374340
Lech Maligranda, The K-functional for symmetric spaces Interpolation Spaces and Allied Topics in Analysis : 29/08/1983 - 01/09/1983. pp. 169- 182 ,(1984) , 10.1007/BFB0099100
Ana M. Vargas, On the maximal function for rotation invariant measures in $ℝ^{n}$ Studia Mathematica. ,vol. 110, pp. 9- 17 ,(1994) , 10.4064/SM-110-1-9-17
E. Stein, Note on the class LlogL Studia Mathematica. ,vol. 32, pp. 305- 310 ,(1969) , 10.4064/SM-32-3-305-310
Elias M. Stein, Singular Integrals and Differentiability Properties of Functions. ,(1971)
M Sharpley, C. Bennett, Interpolation of operators ,(1987)