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- Title
Generalized Sobolev-Shubin spaces, boundedness and Schatten class properties of Toeplitz operators.
- Authors
SANDIKÇI, Ayşe; GÜRKANLI, Ahmet Turan
- Abstract
Let w and ω be two weight functions on ℝ2d and 1 ≤ p, q ≤ ∞. Also let M(p, q, w)(ℝd) denote the subspace of tempered distributions S'(ℝd) consisting of f ∈ S'(ℝd) such that the Gabor transform Vgf of f is in the weighted Lorentz space L (p, q, ω dμ) (ℝ2d). In the present paper we define a space Qg,wM(p,q,w) (ℝd) as counter image of M (p, q, ω) (ℝd) under Toeplitz operator with symbol w. We show that Qg,wM(p,q,w) (ℝd) (ℝd) is a generalization of usual Sobolev-Shubin space Qs(ℝd). We also investigate the boundedness and Schatten-class properties of Toeplitz operators.
- Subjects
TOEPLITZ operators; FUNCTION spaces; MATHEMATICAL bounds; GABOR transforms; LORENTZ spaces; DISTRIBUTION (Probability theory); SET theory
- Publication
Turkish Journal of Mathematics, 2013, Vol 37, Issue 3, p676
- ISSN
1300-0098
- Publication type
Article
- DOI
10.3906/mat-1203-5