Tensor Products of Weighted Bergman Spaces and Invariant Ha-Plitz Operators.
The analytic -capacity and the Cauchy integral
The Banach space H...(X, d, ...).I.
The Banach space H...(X, d, ...).II.
The Bourgain algebra of the disk algebra A(𝔻) and the algebra QA
It is shown that the Bourgain algebra of the disk algebra A() with respect to is the algebra generated by the Blaschke products having only a finite number of singularities. It is also proved that, with respect to , the algebra QA of bounded analytic functions of vanishing mean oscillation is invariant under the Bourgain map as is .
The differential equation y' = fy in the algebras H(D).
The dual of the Bergman space defined on a hyperbolic plane domain.
The Dunford-Pettis property for the ball-algebras, the polydisc-algebras and the Sobolev spaces
The exceptional sets for functions of the Bergman space in the unit ball
Let be a domain in . Given , set . If is a holomorphic and square-integrable function in , then the set of all such that is not square-integrable in has measure zero. We call this set the exceptional set for . In this Note we prove that whenever there exists a holomorphic square-integrable function in the unit ball in such that is the circle .
The Fréchet envelopes of vector-valued Smirnov classes
The generalized corona theorem.
The Gleason-Kahane-Zelazko theorem and function algebras
A theorem due to A. Gleason, J.-P. Kahane and W. Zelazko characterizes continuous characters within the space of all continuous linear forms of a locally multiplicatively convex, sequentially complete algebra. The present paper applies these results to investigate linear isometries of Banach algebras (with particular attention to normal uniform algebras) and of some locally multiplicatively convex algebras. The locally multiplicatively convex algebra of all holomorphic functions on a domain, will...
The metric space , 0
The non-archimedean Corona problem
The norm of uniform convergence on the -algebraic maximal spectrum of an algebra over a non-archimedean valuation field
The projective limit of the spaces
The range of Toeplitz operators on the ball.
The space of multipliers into
The structure of homomorphisms from Banach algebras of differentiable functions into finite dimensional Banach algebras.
The structure of ideals in the Banach algebra of Lipschitz functions over valued fields