Brushlet characterization of the Hardy space H1( R) and the space BMO

Autores: Lasse Borup
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 56, Fasc. 2, 2005, págs. 157-179
Idioma: inglés
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Resumen
- A typical wavelet system constitutes an unconditional basis for various function spaces - Lebesgue, Besov, TriebelLizorkin, Hardy, BMO. One of the main reasons is the frequency localization of an element from such a basis. In this paper we study a wavelettype system, called a brushlet system. In [3] it was noticed that brushlets constitutes unconditional bases for classical function spaces such as the TriebelLizorkin and Besov spaces. In this paper we study brushlet expansions of functions in the Hardy space H1(R) and the space of functions of boundedmean oscillations. We will see that for these spaces we still have a clear similarity between a brushlet and a wavelet expansion.