arXiv subjects

Caiheng Ouyang

Publications and source records attributed to Caiheng Ouyang.

5 recordsLinked to original sources

arXiv2014

Essential Normality of automorphic composition operators

We first characterize those composition operators that are essentially normal on the weighted Bergman space $A^2_s(D)$ for any real $s>-1$, where induced symbols are automorphisms of the unit disk $D$. Using the same technique, we investigate the automorphic composition operators on the Hardy space $H^2(B_N)$ and the weighted Bergman spaces $A^2_s(B_N)$ ($s>-1$). Furthermore, we give some composition operators induced by linear fractional self-maps of the unit ball $B_N$ that are not essentially normal.

math.CV↗

arXiv2012

Carleson measures for Besov-Sobolev spaces with applications in the unit ball of $C^n$

This paper is devoted to give the connections between Carleson measures for Besov-Sobolev spaces $B_p^σ(B)$ and $p$-Carleson measure in the unit ball of ${\bf C}^n$. As applications, we characterize the Riemann-Stieltjes operators and multipliers acting on $B_p^σ(B)$ spaces by means of Carleson measures for $B_p^σ(B)$.

math.CV↗

arXiv2011

Riemann-Stieltjes operators and multipliers on $Q_p$ spaces in the unit ball of $C^n$

This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers acting on M${\rm \ddot{o}}$bius invariant spaces $Q_p$, which unify BMOA and Bloch space in the scale of $p$. The boundedness and compactness of these operators on $Q_p$ spaces are determined by means of an embedding theorem, i.e. $Q_p$ spaces boundedly embedded in the non-isotropic tent type spaces $T_q^\infty$.

math.CV↗

arXiv2010

Compact Differences of Composition Operators on Holomorphic Function Spaces in the Unit Ball

We find a lower bound for the essential norm of the difference of two composition operators acting on $H^2(B_N)$ or $A^2_s(B_N)$ ($s>-1$). This result plays an important role in proving a necessary and sufficient condition for the difference of linear fractional composition operators to be compact, which answers a question posed by MacCluer and Weir in 2005.

math.CV↗

arXiv2008

BMO functions and Carleson measures with values in uniformly convex spaces

This paper studies the relationship between vector-valued BMO functions and the Carleson measures defined by their gradients. Let $dA$ and $dm$ denote Lebesgue measures on the unit disc $D$ and the unit circle $\mathbb T$, respectively. For $1< q<\infty$ and a Banach space $B$ we prove that there exists a positive constant $c$ such that $$\sup_{z_0\in D}\int_{D}(1-|z|)^{q-1}\|\nabla f(z)\|^q P_{z_0}(z) dA(z) \le c^q\sup_{z_0\in D}\int_{\T}\|f(z)-f(z_0)\|^qP_{z_0}(z) dm(z)$$ holds for all trigonometric polynomials $f$ with coefficients in $B$ iff $B$ admits an equivalent norm which is $q$-uniformly convex, where $$P_{z_0}(z)=\frac{1-|z_0|^2}{|1-\bar{z_0}z|^2} .$$ The validity of the converse inequality is equivalent to the existence of an equivalent $q$-uniformly smooth norm.

math.OA↗