Search results for "Bergman space"
showing 5 items of 15 documents
The Bergman projection on weighted spaces: L1and Herz spaces
2002
We nd necessary and sucien t conditions on radial weights w on the unit disc so that the Bergman type projections of Forelli{Rudin are bounded on L 1 (w) and in the Herz spaces K q(w). 1. Introduction and preliminaries. The purpose of this paper is to study spaces of analytic functions on the unit disc D provided with a norm of a weighted Herz space. More precisely we consider the classical family of Bergman projections Ps, s > 1, and we give necessary and sucien t conditions on the weight making these projections continuous in the cor- responding weighted Herz space. We also consider the continuity of these
Group-symmetric holomorphic functions on a Banach space
2016
We study the holomorphic functions on a complex Banach space E that are invariant under the action of a given group of operators on E. A great variety of situations occur depending, of course, on the group and the space. Nevertheless, in the examples we deal with, they can be described in terms of a few natural ones and functions of a finite number of variables. Fil: Aron, Richard. Universidad de Valencia; España Fil: Galindo, Pablo. Universidad de Valencia; España Fil: Pinasco, Damian. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Zalduendo, Ignacio Martin. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de I…
Fractional integration, differentiation, and weighted Bergman spaces
1999
We study the action of fractional differentiation and integration on weighted Bergman spaces and also the Taylor coeffficients of functions in certain subclasses of these spaces. We then derive several criteria for the multipliers between such spaces, complementing and extending various recent results. Univalent Bergman functions are also considered.
Multipliers on Vector Valued Bergman Spaces
2002
AbstractLet X be a complex Banach space and let Bp(X) denote the vector-valued Bergman space on the unit disc for 1 ≤ p < ∞. A sequence (Tn)n of bounded operators between two Banach spaces X and Y defines a multiplier between Bp(X) and Bq(Y) (resp. Bp(X) and lq(Y)) if for any function we have that belongs to Bq(Y) (resp. (Tn(xn))n ∈ lq(Y)). Several results on these multipliers are obtained, some of them depending upon the Fourier or Rademacher type of the spaces X and Y. New properties defined by the vector-valued version of certain inequalities for Taylor coefficients of functions in Bp(X) are introduced.
Spectra and essential spectral radii of composition operators on weighted Banach spaces of analytic functions
2008
AbstractWe determine the spectra of composition operators acting on weighted Banach spaces Hv∞ of analytic functions on the unit disc defined for a radial weight v, when the symbol of the operator has a fixed point in the open unit disc. We also investigate in this case the growth rate of the Koenigs eigenfunction and its relation with the essential spectral radius of the composition operator.