Bergman-Toeplitz operators between weighted L^p-spaces on weakly\n pseudoconvex domains

2019/11/08 by Tran Vu Khanh, Khanh, Tran Vu, Pham Trong Tien +1 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1911.03185

openalex publication_date 2019/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the Bergman-Toeplitz operator T_\ψ induced by\n\ψ(w) = K_\Ω^-\α(w,w)d_\Ω^\β(w) with \α, \β\n\≥ 0 acting from a weighted L^p-space L_a^p(\Ω) to another one\nL_a^q(\Ω) on a large class of pseudoconvex domains of finite type. In the\ncase 1 < p \≤ q < \∞, the following results are established: -\nNecessary and sufficient conditions for boundedness, which generalize the\nrecent results obtained by Khanh, Liu and Thuc. - Upper and lower estimates\nfor essential norm, in particular, a criterion for compactness. - A\ncharacterization of Schatten class membership of this operator on Hilbert space\nL²(\Ω).\n

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