Generalized Sobolev-Shubin spaces, boundedness and Schatten class properties of Toeplitz operators

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Sandıkçı A., Gurkanli A. T.

TURKISH JOURNAL OF MATHEMATICS, vol.37, no.4, pp.676-692, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 4
  • Publication Date: 2013
  • Doi Number: 10.3906/mat-1203-5
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.676-692
  • Keywords: Sobolev-Shubin space, Gabor transform, modulation space, weighted Lorentz space, Toeplitz operators, Schatten-class, MULTIPLIERS, AMALGAMS, LP
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

Let w and omega be two weight functions on R-2d and 1 <= p, q <= infinity. Also let M (p, q, omega) (R-d) denote the subspace of tempered distributions S' (R-d) consisting of f is an element of S' (R-d) such that the Gabor transform V(g)f of f is in the weighted Lorentz space L (p, q, wd mu) (R-2d). In the present paper we define a space Q(g,omega)(M(p,q,omega)) (R-d) as counter image of M (p, q, omega) (R-d) under Toeplitz operator with symbol omega. We show that Q(g,omega)(M(p,q,omega)) (R-d) is a generalization of usual Sobolev-Shubin space Q(s) (R-d). We also investigate the boundedness and Schatten-class properties of Toeplitz operators.