设H,K是复可分的无穷维Hilbert空间。对给定关系A∈BR(H),B∈BR(K),X∈BR(K,H),记2×2上三角关系矩阵MX=(A X 0 B)∈BR(H⊕K),给出Mx的两类点谱σ_(p,1)(M_(X))和σ_(p,2)(M_(X)),两类剩余谱σ_(r,1)(M_(X))和σ_(r,2)(M_(X))与其...设H,K是复可分的无穷维Hilbert空间。对给定关系A∈BR(H),B∈BR(K),X∈BR(K,H),记2×2上三角关系矩阵MX=(A X 0 B)∈BR(H⊕K),给出Mx的两类点谱σ_(p,1)(M_(X))和σ_(p,2)(M_(X)),两类剩余谱σ_(r,1)(M_(X))和σ_(r,2)(M_(X))与其对角元A和B的对应谱的并集之间的联系。展开更多
It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and t...It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.展开更多
Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted...Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).展开更多
In this note,we study a question introduced by Bourin[1]and extend the conclusion from[2]to the case of operators on noncommutative fully symmetric spaces.The conclusion is as follows.Let 0≤x,y∈E(M),If t∈[0,1/4]∪[...In this note,we study a question introduced by Bourin[1]and extend the conclusion from[2]to the case of operators on noncommutative fully symmetric spaces.The conclusion is as follows.Let 0≤x,y∈E(M),If t∈[0,1/4]∪[3/4,1],then∥x^(t)y^(1-t)+ytx^(1-t)∥E(M)≤2^(2t-3/2)∥x+y∥E(M).展开更多
本文刻画了在调和Bergman空间上以| z |2+azm+bz¯n为符号的Toeplitz算子的正规性问题。本文先对调和Bergman空间及Toeplitz算子的相关知识进行了介绍,梳理了调和Bergman空间、Toeplitz算子研究的具有代表性的相关成果。本文还给出...本文刻画了在调和Bergman空间上以| z |2+azm+bz¯n为符号的Toeplitz算子的正规性问题。本文先对调和Bergman空间及Toeplitz算子的相关知识进行了介绍,梳理了调和Bergman空间、Toeplitz算子研究的具有代表性的相关成果。本文还给出了参数相关的以| z |2+azm+bz¯n为符号的Toeplitz算子在调和Bergman空间上的正规性的充分必要条件,在该充要条件的基础上提出了两个推论,建立及推广了该符号下Toeplitz算子的自伴性与正规性的等价关系,补充了这类算子结构性质的相关结论。展开更多
文摘设H,K是复可分的无穷维Hilbert空间。对给定关系A∈BR(H),B∈BR(K),X∈BR(K,H),记2×2上三角关系矩阵MX=(A X 0 B)∈BR(H⊕K),给出Mx的两类点谱σ_(p,1)(M_(X))和σ_(p,2)(M_(X)),两类剩余谱σ_(r,1)(M_(X))和σ_(r,2)(M_(X))与其对角元A和B的对应谱的并集之间的联系。
基金supported by the NSFC(12301115)the Natural Science Foundation of Huzhou(2023YZ11,2024YZ37)the second author was supported by the NSFC(12071437).
文摘It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.
基金supported by the Zhejiang Province Natural Science Foundation of China(LY23A010003).
文摘Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).
基金supported by the Fundamental Research Program of Shanxi Province(202103021223038).
文摘In this note,we study a question introduced by Bourin[1]and extend the conclusion from[2]to the case of operators on noncommutative fully symmetric spaces.The conclusion is as follows.Let 0≤x,y∈E(M),If t∈[0,1/4]∪[3/4,1],then∥x^(t)y^(1-t)+ytx^(1-t)∥E(M)≤2^(2t-3/2)∥x+y∥E(M).
文摘本文刻画了在调和Bergman空间上以| z |2+azm+bz¯n为符号的Toeplitz算子的正规性问题。本文先对调和Bergman空间及Toeplitz算子的相关知识进行了介绍,梳理了调和Bergman空间、Toeplitz算子研究的具有代表性的相关成果。本文还给出了参数相关的以| z |2+azm+bz¯n为符号的Toeplitz算子在调和Bergman空间上的正规性的充分必要条件,在该充要条件的基础上提出了两个推论,建立及推广了该符号下Toeplitz算子的自伴性与正规性的等价关系,补充了这类算子结构性质的相关结论。
