A typical wavelet system constitutes an unconditional basis for various function spaces -Lebesgue, Besov, Triebel-Lizorkin, Hardy, BMO. One of the main reasons is the frequency localization of an element from such a basis. In this paper we study a wavelet-type system, called a brushlet system. In [3] it was noticed that brushlets constitute unconditional bases for classical function spaces such as the Triebel-Lizorkin and Besov spaces. In this paper we study brushlet expansions of functions in the Hardy space H1(R) and the space of functions of bounded mean oscillations. We will see that for these spaces we still have a clear similarity between a brushlet and a wavelet expansion.
@article{urn:eudml:doc:41827,
title = {Brushlet characterization of the Hardy space H1(R) and the space BMO.},
journal = {Collectanea Mathematica},
volume = {56},
year = {2005},
pages = {157-179},
zbl = {1092.42020},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41827}
}
Borup, Lasse. Brushlet characterization of the Hardy space H1(R) and the space BMO.. Collectanea Mathematica, Tome 56 (2005) pp. 157-179. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41827/