Hankel operators on the Dirichlet space

We study (small) Hankel operators on the Dirichlet space D with symbols in a class of function space, and show that such (small) Hankel operators are closely related to the corresponding Hankel operators on the Bergman space and the Hardy space H².     

Composition operators on Dirichlet spaces and Bloch space

In this paper we give a Carleson measure characterization for the compact composition operators between Dirichlet type spaces. We use this characterization to show that every compact composition operator on Dirichlet type spaces is compact on the Bloch space.     

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.     

Composition operators on weighted Dirichlet spaces

We characterize bounded and compact composition operators on weighted Dirichlet spaces. The method involves integral averages of the determining function for the operator, and the connection between composition operators on Dirichlet spaces and Toeplitz operators on Bergman spaces. We also present several examples and counter-examples that point out the borderlines of the result and its connections to other themes.

     

调和Dirichlet空间上小Hankel算子的乘积(英文)

研究了调和Dirichlet空间上调和符号的小Hankel算子的乘积,给出了此类小Hankel算子交换性和乘积为零的完全刻画.     

Cn中有界对称域上不同加权Dirichlet空间之间的复合算子

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔΩｂｅａｂｏｕｎｄｅｄｓｙｍｍｅｔｒｉｃｄｏｍａｉｎｗｉｔｈｉｔｓｓｔａｎｄａｒｄｒｅａｌｉｚａｔｉｏｎｉｎＣｎａｎｄｎｏｒｍａｌｉｚｅｄ（Ｅｕｃｌｉｄｅａｎ）ｖｏｌｕｍｅｍｅａｓｕｒｅｓｏｔｈａｔυ（Ω）＝１．ＬｅｔＫ（·,ｚ）ｄｅｎｏｔｅｔｈｅＢｅｒｇｍａｎｋｅｒｎａｌｆｕｎｃ－ｔｉｏｎａｔｚ∈Ω．ＴｈｅＢｅｒｇｍａｎｍｅｔｒｉｃｏｎΩｉｓｄｅｆｉｎｅｄｂｙＧｚ＝（ｇｉｊ（ｚ））＝１２２ｚｉｚｊｌｏｇＫ（ｚ,ｚ）　１ｉ,ｊｎ．Ｉｆγ：［０,１］…     

Truncations of multilinear Hankel operators

We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are still bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.

     

Weighted Composition Operators on Bergman and Dirichlet Spaces

Let H() denote a functional Hilbert space of analytic functions on a domain . Let w : C and : be such that w f is in H() for every f in H(). The operator wC given by f w f is called a weighted composition operator on H(). In this paper we characterize such operators and those for which (wC )* is a composition operator. Compact weighted composition operators on some functional Hilbert spaces are also characterized. We give sufficient conditions for the compactness of such operators on weighted Dirichlet spaces.     

Composition operators on Dirichlet-type spaces

The Dirichlet-type space ) is the Banach space of functions analytic in the unit disc with derivatives belonging to the Bergman space . Let be an analytic self-map of the disc and define for . The operator is bounded (respectively, compact) if and only if a related measure is Carleson (respectively, compact Carleson). If is bounded (or compact) on , then the same behavior holds on ) and on the weighted Dirichlet space . Compactness on implies that is compact on the Hardy spaces and the angular derivative exists nowhere on the unit circle. Conditions are given which, together with the angular derivative condition, imply compactness on the space . Inner functions which induce bounded composition operators on are discussed briefly.

     

Dirichlet型空间的Carleson测度和乘子

设0-1,D_α~p表示单位球B_n上满足∫_(B_n)(1-|z|~2)~α|▽f(z)|~pdv(z)<∞的全纯函数全体.对0相似文献   

Norm of the Hilbert matrix on Bergman and Hardy spaces and a theorem of Nehari type

The Hilbert matrix induces a bounded operator on most Hardy and Bergman spaces, as was shown by Diamantopoulos and Siskakis. We generalize this for any Hankel operator on Hardy spaces by using a result of Hollenbeck and Verbitsky on the Riesz projection and also compute the exact value of the norm of the Hilbert matrix. Using a new technique, we determine the norm of the Hilbert matrix on a wide range of Bergman spaces.     

The rank of Hankel operators on harmonic Bergman spaces

We show that on the harmonic Bergman spaces, the Hankel operators with nonconstant harmonic symbol cannot be of finite rank.

     

De Branges-Rovnyak spaces and Dirichlet spaces

Sarason has shown that the local Dirichlet spaces Dλ may be considered as manifestations of de Branges-Rovnyak spaces H(b), and has used this identification to give a new proof that the spaces Dλ are star-shaped. We investigate which other Dirichlet spaces D(μ) arise as de Branges-Rovnyak spaces, and which other de Branges-Rovnyak spaces H(b) are star-shaped. We also prove a transfer principle which represents H(b)-spaces inside Dλ.     

On Besov spaces in the Hankel setting

Summary We present new properties of the Besov--Hankel spaces introduced in [10]. We prove a Hankel version of a result of Bui, Paluszyński and Taibleson obtaining new norms that define the topology of the Besov--Hankel spaces. Also we get atomic representations for the distributions in the spaces under consideration.     

Some properties of composition operators on Hilbert spaces of Dirichlet series

In this paper, we study some properties of composition operators on Hilbert spaces of Dirichlet series, which include the Fredholmness, Hilbert-Schmidtness, spectra, cyclic and hypercyclic phenomenons, and also answer a norm question raised by Cowen and MacCluer.     

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.