We study the notion of molecules in coorbit spaces. The main result states that if an operator, originally defined on an appropriate space of test functions, maps atoms to molecules, then it can be extended to a bounded operator on coorbit spaces. For time-frequency molecules we recover some boundedness results on modulation spaces, for time-scale molecules we obtain the boundedness on homogeneous Besov spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-1-6,
author = {Karlheinz Gr\"ochenig and Mariusz Piotrowski},
title = {Molecules in coorbit spaces and boundedness of operators},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {61-77},
zbl = {1167.42007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-1-6}
}
Karlheinz Gröchenig; Mariusz Piotrowski. Molecules in coorbit spaces and boundedness of operators. Studia Mathematica, Tome 192 (2009) pp. 61-77. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-1-6/