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arXiv · 1911.03185

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

Tran Vu Khanh·Pham Trong Tien
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Abstract

In this paper we study the Bergman-Toeplitz operator $T_ψ$ induced by $ψ(w) = K_Ω^{-α}(w,w)d_Ω^β(w)$ with $α, β\geq 0$ acting from a weighted $L^p$-space $L_a^p(Ω)$ to another one $L_a^q(Ω)$ on a large class of pseudoconvex domains of finite type. In the case $1 < p \leq q < \infty$, the following results are established: \\ - Necessary and sufficient conditions for boundedness, which generalize the recent results obtained by Khanh, Liu and Thuc.\\ - Upper and lower estimates for essential norm, in particular, a criterion for compactness.\\ - A characterization of Schatten class membership of this operator on Hilbert space $L^2(Ω)$.

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Tran Vu Khanh, Pham Trong Tien. 2019-11-08. Bergman-Toeplitz operators between weighted $L^p$-spaces on weakly pseudoconvex domains. https://arxiv.org/abs/1911.03185

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