The Modulus of Smoothness in Metric Spaces and Related Problems

被引：0
作者：
Mieczysław Mastyło
机构：
[1] Adam Mickiewicz University Poznań,Faculty of Mathematics and Computer Science
[2] Polish Academy of Sciences (Poznań Branch),Institute of Mathematics
来源：
Potential Analysis | 2011年 / 35卷
关键词：
Metric measure spaces; Modulus of smoothness; Besov space; Hajłasz–Sobolev spaces; Rearrangement estimate; -functional; The Poincaré inequality; Maximal operators; 46E35; 26D10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We define a general variant of the modulus of smoothness in metric spaces and show that under mild condition it is equivalent to the K-functional of a couple of Besov type spaces which in special cases coincide with spaces defined by Korevaar and Schoen. We prove various symmetrization inequalities which involve the modulus, the K-functional and the isoperimetric estimators. We also characterize the Hajłasz-type Sobolev spaces defined not necessarily on doubling measure spaces by means of generalized Poincaré inequalities. This require to study of some variants of the Fefferman–Stein sharp functions as well as the Hardy–Littlewood maximal operators.
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页码：301 / 328
页数：27
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