The Haar wavelet characterization of weighted Herz spaces and greediness of the Haar wavelet basis

Mitsuo Izuki, Yoshihiro Sawano

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

In this paper we consider the Haar wavelet on weighted Herz spaces. Our weight class, whose name is Ap-dyadic local, is the one defined by the first author (2007). We shall investigate the class of Ap-dyadic weights in connection with the maximal inequalities. After obtaining the properties of weights in the first half of the present paper, we consider the Haar wavelet on weighted Herz spaces in the latter half. We shall show that the Haar wavelet basis is an unconditional basis. We also show that the Haar wavelet is not greedy except for the trivial case, that is, the Haar wavelet is greedy if and only if the Herz space under consideration is a weighted Lp space.

Original languageEnglish
Pages (from-to)140-155
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Volume362
Issue number1
DOIs
Publication statusPublished - Feb 1 2010

Keywords

  • Greediness of the Haar wavelet basis
  • The Haar wavelet
  • Weighted Herz spaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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