报告时间：2023年9月24日16：00-18：00

报告地点：北区四号教学楼208

报告题目：Weighted norm inequalities and their applications on vector-valued Fock spaces

报告摘要：In this talk, we characterize the d×d matrix-valued weights W on the complex plane \mathbb{C} such that the Fock projection P_α is bounded on the vector-valued spaces L^2_{(α,W)} (C^d ) induced by W. It is proved that P_α is bounded on L^2_{(α,W)} (C^d ) if and only if W satisfies a restricted A_2-condition. Then we establish some function-theoretic and operator-theoretic properties for the Fock spaces F^2_{(α,W)} (C^d ) induced by the d×d matrix-valued weights W satisfying the restricted A_2-condition: we show that the \mathbb{C}-valued polynomials are dense in F^2_{(α,W)} (C^d ); a Littlwood-Paley formula for F^2_{(α,W)}(C^d ) is established; the bounded diferentiation and integration operators D^(n) :F^2_{(α,W)} (C^d )→L^2 (ΦdA;C^d ) are characterized, where Φ jis a nonnegative matrix-valued function; we also investigate the boundedness of the Volterra type integration operator I_G acting on F^2_{(α,W)}(C^d ), where G is a matrix-valued entire function. in particular, it is shown that for d≥2, T_G may be unbounded on F^2_{(α,W)} (C^d ) when G is a linear polynomial, and I_G may be compact on F^2_{(α,W)} (C^d ) when G is a polynomial of degree greater than 3. These phenomena are in sharp contrast with the case d=1, where I_G is bounded (resp- compact) if and only if G is a polynomial of degree not more than 2 (resp. a linear polynomial).

报告人介绍:王茂发，武汉大学数学与统计学院副院长、教授、博士生导师，全国泛函分析空间理论学术委员会成员、现代分析数学及其应用学术委员会成员，研究领域为泛函分析及其应用，多次承担国家自然科学基金重点、面上等项目，在 Journal of Functional Analysis, Journal of Operator Theory, Mathematische Zeitschrift, Indiana University Mathematics Journal, Science China: Mathematics 等知名期刊上发表学术论文九十余篇。