Nevanlinna and Carleson functions of analytic self‐maps on multiply‐connected domains

In the paper we prove that the Nevanlinna counting function and the Carleson function of analytic self‐maps of finitely connected domains with smooth boundary are equivalent. Using this result we obtain the characterization of compact composition operators on Hardy–Orlicz spaces.     

Holomorphic Campanato type spaces over Carleson tubes and Bergman metric balls

In this paper we give some characterizations of holomorphic Campanato type spaces in terms of Carleson tubes and Bergman metric balls in the unit ball.     

Asymptotic properties of the vector Carleson embedding theorem

The dyadic Carleson embedding operator acting on -valued functions has norm at least . Thus the Carleson Embedding Theorem fails for Hilbert space valued functions.

     

Strong type estimate and Carleson measures for Lipschitz spaces

We establish a capacitary strong type estimate for Lipschitz space and characterize the related Carleson measures.

     

支撑在(-1, 1)上的Carleson型测度与Hankel 矩阵

In this paper, we establish a connection between Carleson type measures supported on(-1, 1) and certain Hankel matrices. The connection is given by the study of Hankel matrices acting on Dirichlet type spaces.     

Carleson measures, multipliers and integration operators for spaces of Dirichlet type

For 0<p<∞ and α>−1, we let denote the space of those functions f which are analytic in the unit disc and satisfy . In this paper we characterize the positive Borel measures μ in D such that , 0<p<q<∞. We also characterize the pointwise multipliers from to (0<p<q<∞) if p−2<α<p. In particular, we prove that if the only pointwise multiplier from to (0<p<q<∞) is the trivial one. This is not longer true for and we give a number of explicit examples of functions which are multipliers from to for this range of values.     

Carleson and sampling measures on Bernstein spaces on Siegel CR manifolds

In this paper, we introduce and study Carleson and sampling measures on Bernstein spaces on a class of quadratic CR manifold called Siegel CR manifolds. These are spaces of entire functions of exponential type whose restrictions to the given Siegel CR manifold are $L^p$-integrable with respect to a natural measure. For these spaces, we prove necessary and sufficient conditions for a Radon measure to be a Carleson or a sampling measure. We also provide sufficient conditions for sampling sequences.     

Weighted BMO and Carleson measures on spaces of homogeneous type

In this paper we characterize the weighted BMO(ω)(X), with X a space of homogeneous type, through an adequate weighted Carleson measure. As a byproduct we can define the weighted Triebel-Lizorkin space and obtain the identification with the above space.     

Carleson measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on complex balls

For 0?σ<1/2 we characterize Carleson measures μ for the analytic Besov-Sobolev spaces on the unit ball Bn in Cn by the discrete tree condition

     

Carleson embeddings and some classes of operators on weighted Bergman spaces

We prove Carleson-type embedding theorems for weighted Bergman spaces with Békollé weights. We use this to study properties of Toeplitz-type operators, integration operators and composition operators acting on such spaces. In particular, we investigate the membership of these operators to Schatten class ideals.     

Growth theorem of convex mappings on bounded convex circular domains

The growth theorem and the 1/2-covering theorem are obtained for the class of normalized biholomorphic convex mappings on bounded convex circular domains, which extend the corresponding results of Sufridge, Thomas, Liu, Gong, Yu, and Wang. The approach is new, which does not appeal to the automorphisms of the domains; and the domains discussed are rather general on which convex mappings can be studied, since the domain may not have a convex mapping if it is not convex. Project supported by the National Natural Science Foundation of China and the State Education Commission Doctoral Foundation.     

Carleson Measures for Besov-Sobolev Spaces with Applications in the Unit Ball of C

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 Cⁿ. 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).     

Carleson测度和多项式逼近

设G是复平面C上的单连通区域,在研究G上的Carleson测度和多项式在G上的Hardy空间Hq(G)中的稠密性问题时,建立起了两者之间的一种等价关系．用Carleson测度给出了多项式在Hq(G)中稠密的充要条件,也刻画了所有那些使得在其上的Carleson测度和Carleson不等式等价的单连通区域．     

Carleson Measures and Toeplitz Operators on Doubling Fock Spaces

Given φ a subharmonic function on the complex plane C,with ?φdA being a doubling measure,the author studies Fock Carleson measures and some characterizations onμsuch that the induced positive Toeplitz operator T_μ is bounded or compact between the doubling Fock space F_φ~p and F_φ~∞ with 0p≤∞,where μ is a positive Borel measure on C.     

A proof of the trace theorem of Sobolev spaces on Lipschitz domains

A complete proof of the trace theorem of Sobolev spaces on Lipschitz domains has not appeared in the literature yet. The purpose of this paper is to give a complete proof of the trace theorem of Sobolev spaces on Lipschitz domains by taking advantage of the intrinsic norm on . It is proved that the trace operator is a linear bounded operator from to for .

     

Area operators from H~p spaces to L~q spaces

We characterize non-negative measures μ on the unit disk D for which the area operator A μ is bounded or compact from Hardy space H p to L q (D) spaces.     

Schwarzian derivative and general Besov-type domains

We study univalent functions f for which belongs to a class of general Besov-type spaces. We give a characterization of the general Besov-type domains in terms of Carleson measure conditions on the Schwarzian derivative Sf, and mention some further connection to Teichmüller theory.