Lions-Peetre’s interpolation methods associated with quasi-power functions and some applications

Document identifier: oai:dalea.du.se:1930
Access full text here:10.1216/rmjm/1181069378
Keyword: Natural Sciences, Mathematics, Naturvetenskap, Matematik, Besov-Orlicz space; commutator; Lions-Peetre's interpolation method; multi-dimensional uniform rotundity; quasi-power; Schatten-Orlicz class; strong phi-variation; Triebel-Lizorkin-Orliez space
Publication year: 2006
Abstract:

This paper concerns some properties of Lions-Peetre's interpolation methods of constants and means associated with quasi-power functions, and their applications in harmonic analysis, martingale inequalities, and geometric properties of Banach spaces. We describe Besov-Orlicz spaces and Triebel-Lizorkin-Orlicz spaces in terms of interpolation and wavelet bases. We study the commutators of quasi-logarithmic operators and singular integral operators, Hankel operators in Schatten-Orlicz classes, martingale inequalities for the partial derivative-variation, and the stability of multi-dimensional uniform rotundity under interpolation.

Authors

Ming Fan

Högskolan Dalarna; Matematik/tillämpad matematik
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