报告人：章珂南 博士生（复旦大学）

时间：2026年06月05日 16:10-

地点：理科楼LA104

摘要：Shimorin-type kernels naturally appear in the representation of kernels for log-subharmonic weighted Bergman spaces, as first observed by Shimorin in 2002.

First we discuss a converse problem of Shimorin's kernel representation theorem: determining when a Shimorin-type kernel actually arises from a radial log-subharmonic weighted Bergman space. This problem is reduced to conditions involving moment sequences and log-convexity. We then turn to the $L^p-L^q$ estimates for the associated integral operator.

Inspired by classical Bergman-type operators, we identify the boundary line $\mathcal{C}$ between the $L^p$-$L^q$ boundedness and unboundedness regions. Finally, we discuss the more delicate behavior on the critical line and give a characterization of when the operator satisfies standard Bergman-type estimates.

This report concludes with future directions concerning one-weight inequalities for weighted Bergman projections.

邀请人：算子理论团队

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