Fractional operator and Carleson measure in Fock spaces

摘要: In this talk, we present a comprehensive study of fractional calculus in weighted Fock spaces. We focus on three key aspects:

1、Establishing precise criteria for the boundedness of fractional integral operators, based on operator order, weight parameters, and exponent relationships.

2、Characterizing the boundedness of fractional Volterra operators, linked to polynomial constraints and inequalities involving space weights and exponents.

3、Providing a complete geometric description of fractional Carleson measures, integrating measure-theoretic and operator-theoretic perspectives.

Our analysis employs kernel estimates, atomic decomposition, and duality, offering a unified framework for studying fractional operators in Fock spaces.

报告人简介：侯绳照，苏州大学数学学院教授，博士生导师，主要从事函数空间上的算子理论及相关问题研究。在函数空间的分析和几何结构及相关算子的有界性研究方面得到一系列系统的结果，已经主持完成多项国家自然科学基金项目。