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Molecules in coorbit spaces and boundedness of operators

Karlheinz Gröchenig;  Mariusz Piotrowski — 2009

Studia Mathematica

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.

Non-smooth atomic decompositions of anisotropic function spaces and some applications

Susana D. Moura;  Iwona Piotrowska;  Mariusz Piotrowski — 2007

Studia Mathematica

The main purpose of the present paper is to extend the theory of non-smooth atomic decompositions to anisotropic function spaces of Besov and Triebel-Lizorkin type. Moreover, the detailed analysis of the anisotropic homogeneity property is carried out. We also present some results on pointwise multipliers in special anisotropic function spaces.

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