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.
引用
收藏
页码：301 / 328
页数：27
相关论文
共 55 条
[1]  
Bastero J(2000)Rearrangement of Hardy–Littlewood maximal functions in Lorentz spaces Proc. Am. Math. Soc. 128 65-74
[2]  
Milman M(2003)A note on Indiana Univ. Math. J. 52 1215-1230
[3]  
Ruiz FJ(1981)(0, Ann. Math. 113 601-611
[4]  
Bastero J(1975)) spaces and Sobolev embeddings Invent. Math. 30 265-284
[5]  
Milman M(2005)Weak- J. Funct. Anal. 229 375-404
[6]  
Ruiz FJ(1998) and J. Funct. Anal. 153 108-146
[7]  
Bennett C(2010)The Brunn–Minkovswi inequality in Gauss space Math. Nachr. 283 215-231
[8]  
DeVore R(1996)Functional properties of rearrangement invariant spaces defined in terms of oscillations Potential Anal 5 403-415
[9]  
Sharpley R(1998)Self-improving properties of John–Nirembetg and Poincaré inequalities on spaces of homogeneous type Rev. Mat. Iberoam. 14 601-622
[10]  
Borell C(2006)Interpolation properties of Besov spaes defined on metric spaces Math. Z. 254 591-609
123456