Local characterization of generalized 2-microlocal spaces

Preprint series: 06-23, Analysis

The paper is published: Jenaer Schriften zur Mathematik und Informatik 20/06

MSC:
42B35 Function spaces arising in harmonic analysis
42B25 Maximal functions, Littlewood-Paley theory
42B15 Multipliers

Abstract: This paper deals with a generalization of 2-microlocal spaces in the sense of weighted Besov spaces. We define 2-microlocal Besov spaces \$B^{s,{mloc}}_{pq}(\\mathb{R}^n,w)\$ and describe first properties.
The key theorem is the local means characterization for these spaces. Using this characterization we prove some conclusions as a pointwise multiplier assertion and the invariance of the spaces \$B^{s,{mloc}}_{pq}(\\mathb{R}^n,w)\$ under the action of diffeomorphisms.

Keywords: Besov spaces, 2-microlocal spaces, local means