Generalized Sobolev-Shubin Spaces, Boundedness and Schatten Class Properties of Toeplitz Operators

Abstract

Let ω and ω be two weight functions on ℝ2d and 1 = p, q = 8. Also let M (p, q, ω) (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, ωdμ) (ℝ2d) . In the present paper we define a space QM(p,q,ω) <inf>g,w</inf> (ℝd) as counter image of M (p, q, ω) (ℝd) under Toeplitz operator with symbol w. We show that QM(p,q,ω) <inf>g,w</inf> (ℝd) is a generalization of usual Sobolev-Shubin space Qs (ℝd). We also investigate the boundedness and Schatten-class properties of Toeplitz operators. © TÜBİTAK.