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Journals / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 4

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

Ahmet Turan GÜRKANLI
Ayşe SANDIKÇI
Pages
676–692
Publication Date
2022-11-03
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also investigate the boundedness and Schatten-class properties of Toeplitz operators.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let w and w be two weight functions on R2d and 1 \leq p,q \leq \infty.
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Key Findings & Data: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) .
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Conclusion & Impact:We also investigate the boundedness and Schatten-class properties of Toeplitz operators.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Sobolev-Shubin space · Gabor transform · modulation space

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.

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.

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Cite This Article

GÜRKANLI, A. T., SANDIKÇI, A. (2022). Generalized Sobolev-Shubin spaces, boundedness and Schatten class properties of Toeplitz operators. Turkish Journal of Mathematics, Cilt: 37 - Sayı: 4, 676–692. https://ajindex.com/articles/608301

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