解析Morrey空间上的积分算子

从解析Morrey空间到Bloch空间的Volterra型算子

Volterrra-type Operators from analytic Morrey spaces to Bloch space

本文研究了从解析Morrey空间到Bloch空间的积分算子$I_g$和$T_g $的有界性和紧性.进一步给出了这些算子的范数和本质范数。

Boundedness And Compactness Of Cauchy-Type Integral Commutator On Weighted Morrey Spaces

In this paper we study the boundedness and compactness characterizations of the commutator of Cauchy type integrals $\mathcal C$ on a bounded strongly pseudoconvex domain $D$ in $C^n$ with boundary $bD$ satisfying the minimum regularity condition $C^{2}$ based on the recent result of Lanzani-Stein and Duong-Lacey-Li-Wick-Wu. We point out that in this setting the Cauchy type integral $\mathcal C$ is the sum of the essential part $\mathcal{C}^\sharp$ which is a Calderón-Zygmund operator and a remainder $\mathcal R$ which is no longer a Calderón-Zygmund operator. We show that the commutator $[b, …

Semigroups of composition operators in analytic Morrey spaces

Analytic Morrey spaces belong to the class of function spaces which, like BMOA, are defined in terms of the degree of oscillation on the boundary of functions analytic in the unit disc. We consider semigroups of composition operators on these spaces and focus on the question of strong continuity. It is shown that these semigroups behave like on BMOA.

Burkholder积分、Morrey问题与拟共形映射

Burkholder integrals, Morrey's problem and quasiconformal mappings

受Morrey问题（秩一凸泛函）和Burkholder积分（他的鞅理论）的启发，我们发现，Burkholder泛函$B_p$，$p \ge 2$，是拟凹的，当测试的变形身份$f\in Id + C^\infty_0(Ω)$与$B_p(Df(x)) \ge 0$逐点，或等效的，变形，使$|Df|^2 \leq \frac{p}{p-2} J_f$。特别地，这在恒等映射的显式邻域中成立。在许多直接的后果，这给出了最强的可能$L^p$ -贝尔特拉米方程$\f_{\bar{z}} = μ(z) f_z$的主解的梯度估计，对于任何$p$在临界区间$2 \leq p \leq 1+1/\|μ_f\|_\infty$。缺乏对称性的局部最大值的例子表明了问题的复杂性。

某些解析函数空间的伪解析扩张

The pseudoanalytic extensions for some spaces of analytic functions

利用Cauchy-Riemann算子，我们用原函数的伪解析扩张刻画了$Q_K$空间、Besov空间和解析Morrey空间.我们的结果在一些经典的Banach空间，如Bloch空间，$BMOA$和Dirichlet空间上也成立.

临界$Q$空间的解析形式及其性质

Analytic version of critical $Q$ spaces and their properties

本文建立了单位圆盘$\mathbb{D}$上临界空间$Q_α^β(\mathbb{R}^{n})$的解析形式，记作$Q^β_{p}(\mathbb{D})$ .进一步证明了$Q^β_{p}(\mathbb{D})$与Morrey空间之间的关系。利用两个积分算子的有界性，给出了$Q^β_{p}(\mathbb{D})$的乘子空间.