Molecules in coorbit spaces and boundedness of operators
Volume 192 / 2009
Studia Mathematica 192 (2009), 61-77
MSC: 42B35, 46E35.
DOI: 10.4064/sm192-1-6
Abstract
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.
