Divisibility Structure and Finitely Generated Ideals in the Disc Algebra.
Domains with Finite Dimensional Bergman Space.
Douglas algebras without maximal subalgebra and without minimal superalgebra.
Duals to weighted spaces of analytic functions.
Dynamics of complex singularities in 1D nonlinear parabolic PDE's
We establish local-in-time smoothing of a simple model nonlinear parabolic PDE in a scale of weighted Bergman spaces on a strip provided the weights are not too singular. This constitutes a very strong smoothing property since an immediate consequence is that the PDE can "push away" an algebraic-type complex singularity provided that the order of the singularity is small enough.
Dynamics of composition operators in analytic functional Hilbert spaces. (Dinámica de operadores de composición en espacios de Hilbert funcionales analíticos.)
Ein Approximationssatz für holomorphe Funktionen auf nicht-kompakte Riemannschen Flächen.
Ein funktionalanalytischer Beweis des Approximationssatzes von Walsh.
Embedding polydisk algebras into the disk algebra and an application to stable ranks
It is shown how to embed the polydisk algebras (finite and infinite ones) into the disk algebra A(𝔻̅). As a consequence, one obtains uniform closed subalgebras of A(𝔻̅) which have arbitrarily prescribed stable ranks.
Erratum to: "Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces" (Studia Math. 213 (2012), 169-187)
Essential norm and a new characterization of weighted composition operators from weighted Bergman spaces and Hardy spaces into the Bloch space
In this paper, we give some estimates for the essential norm and a new characterization for the boundedness and compactness of weighted composition operators from weighted Bergman spaces and Hardy spaces to the Bloch space.
Essential norm of the difference of composition operators on Bloch space
Let and be holomorphic self-maps of the unit disk, and denote by , the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators from Bloch spaces to Bloch spaces in the unit disk. Compactness of the difference is also characterized.
Essential norm of weighted composition operator between -Bloch space and -Bloch space in polydiscs.
Essential normality for certain finite linear combinations of linear-fractional composition operators on the Hardy space
In 1999 Nina Zorboska and in 2003 P. S. Bourdon, D. Levi, S. K. Narayan and J. H. Shapiro investigated the essentially normal composition operator , when is a linear-fractional self-map of . In this paper first, we investigate the essential normality problem for the operator on the Hardy space , where is a bounded measurable function on which is continuous at each point of , , and is the Toeplitz operator with symbol . Then we use these results and characterize the essentially normal...
Essential norms of weighted composition operators between Hardy spaces and for 1 ≤ p,q ≤ ∞
We complete the different cases remaining in the estimation of the essential norm of a weighted composition operator acting between the Hardy spaces and for 1 ≤ p,q ≤ ∞. In particular we give some estimates for the cases 1 = p ≤ q ≤ ∞ and 1 ≤ q < p ≤ ∞.
Essential spectra of weighted composition operators with hyperbolic symbols
In this paperwe study both the spectra and the essential spectra ofweighted composition operators on Hardy spaces Hp(ⅅ), standard weighted Bergman spaces Apα(ⅅ) and weighted H∞1-type spaces when the symbols are of hyperbolic type
Estimates in the Hardy-Sobolev space of the annulus and stability result
The main purpose of this work is to establish some logarithmic estimates of optimal type in the Hardy-Sobolev space ; of an annular domain. These results are considered as a continuation of a previous study in the setting of the unit disk by L. Baratchart and M. Zerner, On the recovery of functions from pointwise boundary values in a Hardy-Sobolev class of the disk, J. Comput. Appl. Math. 46 (1993), 255–269 and by S. Chaabane and I. Feki, Optimal logarithmic estimates in Hardy-Sobolev spaces...
Exposed points in the set of representing measures for the disc algebra
It is shown that for each nonzero point x in the open unit disc D, there is a measure whose support is exactly ∂D ∪ {x} and that is also a weak*-exposed point in the set of representing measures for the origin on the disc algebra. This yields a negative answer to a question raised by John Ryff.
Extension maps in ultradifferentiable and ultraholomorphic function spaces
The problem of the existence of extension maps from 0 to ℝ in the setting of the classical ultradifferentiable function spaces has been solved by Petzsche [9] by proving a generalization of the Borel and Mityagin theorems for -spaces. We get a Ritt type improvement, i.e. from 0 to sectors of the Riemann surface of the function log for spaces of ultraholomorphic functions, by first establishing a generalization to some nonclassical ultradifferentiable function spaces.
Extension of Zhu's solution to Lotto's conjecture on the weighted Bergman spaces.