Geodesic
Molecules in coorbit spaces and boundedness of operators
Karlheinz Gröchenig 1   ; Mariusz Piotrowski 1
1 Faculty of Mathematics University of Vienna Nordbergstrasse 15 A-1090 Vienna, Austria
Studia Mathematica, Tome 192 (2009) no. 1, pp. 61-77 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm192-1-6
Keywords: study notion molecules coorbit spaces main result states operator originally defined appropriate space test functions maps atoms molecules extended bounded operator coorbit spaces time frequency molecules recover boundedness results modulation spaces time scale molecules obtain boundedness homogeneous besov spaces

Karlheinz Gröchenig  1   ; Mariusz Piotrowski  1

1 Faculty of Mathematics University of Vienna Nordbergstrasse 15 A-1090 Vienna, Austria 
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Karlheinz Gröchenig; Mariusz Piotrowski. Molecules in coorbit spaces and boundedness of operators. Studia Mathematica, Tome 192 (2009) no. 1, pp. 61-77. doi: 10.4064/sm192-1-6

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