Kernel theorems in coorbit theory

We prove general kernel theorems for operators acting between coorbit spaces. These are Banach spaces associated to an integrable representation of a locally compact group and contain most of the usual function spaces (Besov spaces, modulation spaces, etc.). A kernel theorem describes the form of ev...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society. Series B 2019-11, Vol.6 (11), p.346-364
Main Authors: Balazs, Peter, Gröchenig, Karlheinz, Speckbacher, Michael
Format: Article
Language:English
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Summary:We prove general kernel theorems for operators acting between coorbit spaces. These are Banach spaces associated to an integrable representation of a locally compact group and contain most of the usual function spaces (Besov spaces, modulation spaces, etc.). A kernel theorem describes the form of every bounded operator between a coorbit space of test functions and distributions by means of a kernel in a coorbit space associated to the tensor product representation. As special cases we recover Feichtinger's kernel theorem for modulation spaces and the recent generalizations by Cordero and Nicola. We also obtain a kernel theorem for operators between the Besov spaces \dot {B}^0_{1,1} and \dot {B}^{0}_{\infty , \infty }.
ISSN:2330-0000
2330-0000
DOI:10.1090/btran/42