scholarly journals Compactness of Composition Operators on the Bergman Spaces of Convex Domains and Analytic Discs

2021 ◽  
Author(s):  
T. G. Clos
Keyword(s):  
Composition Operators ◽  
Bergman Spaces ◽  
Convex Domains ◽  
Analytic Discs

scholarly journals Compact Differences of Composition Operators on Bergman Spaces Induced by Doubling Weights

2021 ◽  
Author(s):  
Bin Liu ◽  
Jouni Rättyä ◽  
Fanglei Wu
Keyword(s):  
Bergman Space ◽  
Open Problem ◽  
Lebesgue Space ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Carleson Measures ◽  
Doubling Weights ◽  
The Way

AbstractBounded and compact differences of two composition operators acting from the weighted Bergman space $$A^p_\omega $$ A ω p to the Lebesgue space $$L^q_\nu $$ L ν q , where $$0<q<p<\infty $$ 0 < q < p < ∞ and $$\omega $$ ω belongs to the class "Equation missing" of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proofs a new description of q-Carleson measures for $$A^p_\omega $$ A ω p , with $$p>q$$ p > q and "Equation missing", involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space $$A^p_\alpha $$ A α p with $$-1<\alpha <\infty $$ - 1 < α < ∞ to the setting of doubling weights. The case "Equation missing" is also briefly discussed and an open problem concerning this case is posed.

scholarly journals Hardy and Bergman spaces on hyperconvex domains and their composition operators

2008 ◽  
Vol 57 (5) ◽  
pp. 2153-2202 ◽  
Author(s):  
Evgeny A. Poletsky ◽  
Michael I. Stessin
Keyword(s):  
Composition Operators ◽  
Bergman Spaces ◽  
Hardy And Bergman Spaces

scholarly journals Gain of Regularity in Extension Problem on Convex Domains

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
M. Jasiczak
Keyword(s):  
Finite Type ◽  
Bergman Space ◽  
Bergman Spaces ◽  
Extension Problem ◽  
Convex Domains

We investigate the extension problem from higher codimensional linear subvarieties on convex domains of finite type. We prove that there exists a constantdsuch that on Bergman spacesHp(D)with1≤p<dthere appears the so-called “gain regularity.” The constantddepends on the minimum of the dimension and the codimension of the subvariety. This means that the space of functions which admit an extension to a function in the Bergman spaceHp(D)is strictly larger thanHp(D∩A), whereAis a subvariety.

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