Bulletin of the Australian Mathematical Society

Table of Contents - August 2009 - Volume 80, Issue 01  

Research Article

SHARPNESS OF SOME PROPERTIES OF WIENER AMALGAM AND MODULATION SPACES

ELENA CORDEROa1 c1 and FABIO NICOLAa2

a1 Department of Mathematics, University of Torino, Via Carlo Alberto 10, 10123 Torino, Italy (email: elena.cordero@unito.it)

a2 Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy (email: fabio.nicola@polito.it)

Abstract

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.

(Received September 04 2008)

2000 Mathematics subject classification

  • primary 42B35; secondary 46E35

Keywords and phrases

  • Wiener amalgam spaces;
  • modulation spaces;
  • dilation operator

Correspondence:

c1 For correspondence; e-mail: elena.cordero@unito.it