Dergiler / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 4
Generalized Sobolev-Shubin spaces, boundedness and Schatten class properties of Toeplitz operators
- Sayfa
- 676–692
- DOI
- —
Özet
Let w and w be two weight functions on R2d and 1 \leq p,q \leq \infty. Also let M(p,q,w) (Rd) denote the subspace of tempered distributions S' (Rd) consisting of f \in S' (Rd) such that the Gabor transform Vg f of f is in the weighted Lorentz space L(p,q,w dm) (R2d) . In the present paper we define a space Qg,w^{M(p,q,w) (R^d) as counter image of M(p,q,w) (R^d) under Toeplitz operator with symbol w. We show that Qg,w^{M(p,q,w)}(R^d) is a generalization of usual Sobolev-Shubin space Qs (R^d). We also investigate the boundedness and Schatten-class properties of Toeplitz operators.
Abstract
Let w and w be two weight functions on R2d and 1 \leq p,q \leq \infty. Also let M(p,q,w) (Rd) denote the subspace of tempered distributions S' (Rd) consisting of f \in S' (Rd) such that the Gabor transform Vg f of f is in the weighted Lorentz space L(p,q,w dm) (R2d) . In the present paper we define a space Qg,w^{M(p,q,w) (R^d) as counter image of M(p,q,w) (R^d) under Toeplitz operator with symbol w. We show that Qg,w^{M(p,q,w)}(R^d) is a generalization of usual Sobolev-Shubin space Qs (R^d). We also investigate the boundedness and Schatten-class properties of Toeplitz operators.