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SHARPNESS OF SOME PROPERTIES OF WIENER AMALGAM AND MODULATION SPACES

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  19 June 2009

ELENA CORDERO  and
FABIO NICOLA
ELENA CORDERO*
Affiliation:
Department of Mathematics, University of Torino, Via Carlo Alberto 10, 10123 Torino, Italy (email: elena.cordero@unito.it)
FABIO NICOLA
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy (email: fabio.nicola@polito.it)
*
✉For correspondence; e-mail: elena.cordero@unito.it
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Abstract

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We prove sharp estimates for the dilation operator f(x)⟼f(λx), when acting on Wiener amalgam spaces W(Lp,Lq). Scaling arguments are also used to prove the sharpness of the known convolution and pointwise relations for modulation spaces Mp,q, as well as the optimality of an estimate for the Schrödinger propagator on modulation spaces.

Keywords

Wiener amalgam spacesmodulation spacesdilation operator

MSC classification

Secondary: 42B35: Function spaces arising in harmonic analysis
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 1 , August 2009 , pp. 105 - 116
Copyright
Copyright © Australian Mathematical Society 2009

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