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 language | English |
|---|---|
| Pages (from-to) | 140-155 |
| Number of pages | 16 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 362 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 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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Izuki, M., & Sawano, Y. (2010). The Haar wavelet characterization of weighted Herz spaces and greediness of the Haar wavelet basis. Journal of Mathematical Analysis and Applications, 362(1), 140-155. https://doi.org/10.1016/j.jmaa.2009.08.005