Similarity of analytic Toeplitz operators on the Bergman spaces

In this paper we give a function theoretic similarity classification for Toeplitz operators on weighted Bergman spaces with symbol analytic on the closure of the unit disk.     

On Blaschke products with derivatives in Bergman spaces with normal weights

We generalize a well-known sufficient condition for interpolating sequences for the Hilbert Bergman spaces to other Bergman spaces with normal weights (as defined by Shields and Williams) and obtain new results regarding the membership of the derivative of a Blaschke product or a general inner function in such spaces. We also apply duality techniques to obtain further results of this type and obtain new results about interpolating Blaschke products.     

A note on weighted composition operators on the weighted Bergman space

This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space only with bounded weighted symbols if and only if the composition symbol is a finite Blaschke product.     

共形空间${\mathbb Q}^n_s$中的正则Blaschke拟全脐子流形

[Nie C X,Wu C X,Regular submanifolds in the conformal space Q_p~n,ChinAnn Math,2012,33B(5):695-714]中研究了共形空间Q_s~n中的正则子流形,并引入了共形空间Q_s~n中的子流形理论.本文作者将分类共形空间Q_s~n中的Blaschke拟全脐子流形,证明伪Riemann空间形式中具有常数量曲率和平行的平均曲率向量场的正则子流形是共形空间中的Blaschke拟全脐子流形;反之,共形空间中的Blaschke拟全脐子流形共形等价于伪Riemann空间形式中具有常数量曲率和平行的平均曲率向量场的正则子流形.这一结论可看作是共形空间Q_s~n中共形迷向子流形分类定理的推广.     

A Formula for Submanifolds in S~n and Its Applications in Moebius Geometry

1 IlitroductionIn [1], Mg ChangPing established a new frame for Moebius goometry Of submbofOlds inunit sphere. He defined Moebius invariant metric g! Blaschk tensor A, Moebius secondfUndamental form B, and Moebius fOrm ., and established the structure eqllations. Basedon this Foundation, Liu Huili, Wang ChangPing and Zhao Guosong have given the classification Of the Moebius isotropic submanifOlds in Sn (x is said to be Moebius isotropic if. = 0and A == Ag for some smooth function A…     

A Singular Riesz Product in the Nevai Class and Inner Functions with the Schur Parameters in ∩p>2 l

There exist singular Riesz products dσ=∏^∞_κ=1 (1+Re(α_κζ^n_κ)) on the unit circle with the parameters (a_n)_n0 of orthogonal polynomials in L²(dσ) satisfying ∑^∞_n=0 |a_n|^p<+∞ for every p, p>2. The Schur parameters of the inner factor of the Cauchy integral ∫ (ζ−z)⁻¹ dσ(ζ), σ being such a Riesz product, belong to ∩_p>2 l^p.