Estudiamos algunas cuestiones estructurales acerca del espacio localmente convexo HV∞, que está formado por funciones analíticas en el disco unidad abierto. Construimos una descomposición atómica de este espacio, usando un retículo de puntos del disco unidad que es más denso que el usual. También demostramos que HV∞ no es nuclear.
Résumé. Soient D un ouvert de ℂ et E un compact de D. Moyennant une hypothèse assez faible sur D et ℂ̅ E on montre que si α ∈ ]0,1[ vérifie , étant l’ouvert de niveau z ∈ D : ω(E,D,z) < α, alors toute base commune de O(E) et O(D) est une base de .
Given 0 < p,q < ∞ and any sequence z = zₙ in the unit disc , we define an operator from functions on to sequences by . Necessary and sufficient conditions on zₙ are given such that maps the Hardy space boundedly into the sequence space . A corresponding result for Bergman spaces is also stated.
We characterize Carleson measures for the analytic Besov spaces. The problem is first reduced to a discrete question involving measures on trees which is then solved. Applications are given to multipliers for the Besov spaces and to the determination of interpolating sequences. The discrete theorem is also applied to analysis of function space on trees.
We study connected components of a common zero set of equivalent singular inner functions in the maximal ideal space of the Banach algebra of bounded analytic functions on the open unit disk. To study topological properties of zero sets of inner functions, we give a new type of factorization theorem for inner functions.
Let ,B and Qβ be the weighted Nevanlinna space, the Bloch space and the Q space, respectively. Note that B and are Möbius invariant, but is not. We characterize, in function-theoretic terms, when the composition operator induced by an analytic self-map ϕ of the unit disk defines an operator , , which is bounded resp. compact.
H. Jiang and C. Lin [Chinese Ann. Math. 23 (2002)] proved that there exist infinitely many Banach spaces, called refined Besov spaces, lying strictly between the Besov spaces and . In this paper, we prove a similar result for the analytic Besov spaces on the unit disc . We base our construction of the intermediate spaces on operator theory, or, more specifically, the theory of symmetrically normed ideals, introduced by I. Gohberg and M. Krein. At the same time, we use these spaces as models to...
This paper characterizes the Banach algebras of continuous functions on which the spectral factorization mapping 𝔖 is continuous or bounded. It is shown that 𝔖 is continuous if and only if the Riesz projection is bounded on the algebra, and that 𝔖 is bounded only if the algebra is isomorphic to the algebra of continuous functions. Consequently, 𝔖 can never be both continuous and bounded, on any algebra under consideration.
Let φ and ψ be analytic self-maps of 𝔻. Using the pseudo-hyperbolic distance ρ(φ,ψ), we completely characterize the boundedness and compactness of the difference of generalized weighted composition operators between growth spaces.