Mobius-Invariant Spaces of Continuous Functions
Monge-Ampère measures and Poletsky-Stessin Hardy spaces on bounded hyperconvex domains
Poletsky-Stessin Hardy (PS-Hardy) spaces are the natural generalizations of classical Hardy spaces of the unit disc to general bounded, hyperconvex domains. On a bounded hyperconvex domain Ω, the PS-Hardy space is generated by a continuous, negative, plurisubharmonic exhaustion function u of the domain. Poletsky and Stessin considered the general properties of these spaces and mainly concentrated on the spaces where the Monge-Ampère measure has compact support for the associated exhaustion...
Multiplication operators on Bergman spaces.
Multiplicative isometries on the Smirnov class
We show that T is a surjective multiplicative (but not necessarily linear) isometry from the Smirnov class on the open unit disk, the ball, or the polydisk onto itself, if and only if there exists a holomorphic automorphism Φ such that T(f)=f ○ Φ for every class element f or T(f) = for every class element f, where the automorphism Φ is a unitary transformation in the case of the ball and Φ(z 1, ..., z n) = for |λ j| = 1, 1 ≤ j ≤ n, and (i 1; ..., i n)is some permutation of the integers from...
Multipliers of de Branges-Rovnyak spaces in H2.
In 1966 de Branges and Rovnyak introduced a concept of complementation associated to a contraction between Hilbert spaces that generalizes the classical concept of orthogonal complement. When applied to Toeplitz operators on the Hardy space of the disc, H2, this notion turned out to be the starting point of a beautiful subject, with many applications to function theory. The work has been in constant progress for the last few years. We study here the multipliers of some de Branges-Rovnyak spaces...
-type quotient modules on the torus.
New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces
Let be a holomorphic function and a holomorphic self-map of the open unit disk in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators from Zygmund type spaces to Bloch type spaces in in terms of , , their derivatives, and , the -th power of . Moreover, we obtain some similar estimates for the essential norms of the operators , from which sufficient and necessary conditions of compactness of follows immediately.
New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space
Let ψ and φ be analytic functions on the open unit disk with φ() ⊆ . We give new characterizations of the bounded and compact weighted composition operators W ψ,ϕ from the Hardy spaces H p, 1 ≤ p ≤ ∞, the Bloch space B, the weighted Bergman spaces A αp, α > − 1,1 ≤ p < ∞, and the Dirichlet space to the Bloch space in terms of boundedness (respectively, convergence to 0) of the Bloch norms of W ψ,ϕ f for suitable collections of functions f in the respective spaces. We also obtain characterizations...
Noncoherence of a causal Wiener algebra used in control theory.
Nouvelles propriétés des espaces et
Numerical range of operators acting on Banach spaces
The aim of the paper is to propose a definition of numerical range of an operator on reflexive Banach spaces. Under this definition the numerical range will possess the basic properties of a canonical numerical range. We will determine necessary and sufficient conditions under which the numerical range of a composition operator on a weighted Hardy space is closed. We will also give some necessary conditions to show that when the closure of the numerical range of a composition operator on a small...
Obtainment of the norm in Bergman spaces.
On a class of composition operators on Bergman space.
On an Estimate of Axler and Shapiro.
On Bloch functions and normal functions.
On BMO-type characteristics for one class of holomorphic functions in a disk.
On completeness with respect to a Carathéodory-like metric
On cyclicity in weighted Dirichlet spaces.
On Dominating Sequences in the Unit Disc.
On extended eigenvalues and extended eigenvectors of truncated shift
In this paper we consider the truncated shift operator Su on the model space K2u := H2 θ uH2. We say that a complex number λ is an extended eigenvalue of Su if there exists a nonzero operator X, called extended eigenvector associated to λ, and satisfying the equation SuX = λXSu. We give a complete description of the set of extended eigenvectors of Su, in the case of u is a Blaschke product..