8 papers · 1 filter
Critical cyclicity in Dirichlet-type spaces on the bidisk
Athanasios Beslikas, Pouriya Torkinejad Ziarati
Consider the Dirichlet-type spaces on the bidisc defined by $$\mathcal{D}_β(\mathbb{D}^2)=\Bigg\{f(z_1,z_2)=\sum_{k,l}a_{kl}z_1^kz_2^l\in\mathcal{O}(\mathbb{D}^2): \sum_{k,l\ge 0}|…
Composition operators and Rational Inner Functions on the bidisc: A geometric approach
Athanasios Beslikas
We study composition operators acting on the weighted Bergman spaces on the bidisc, i.e. where is induced by rational inner fun…
On the membership of two-variable Rational Inner Functions in spaces of Dirichlet-type
Athanasios Beslikas, Alan Sola
We study membership of rational inner functions on the bidisk in a scale of Dirichlet spaces considered by Bera, Chavan, and Ghara, and in higher-order variants of t…
Composition Operators and Rational Inner Functions II: Boundedness between two different Bergman Spaces
Athanasios Beslikas
In this note we provide a sufficient condition on when the composition operator is bounded, whenever and is positive…
Composition operators and Rational Inner Functions on the bidisc
Athanasios Beslikas
In the present article, composition operators induced by Rational Inner Functions on the bidisc are studied, acting on the weighted Bergman space $A^2_β(\mathbb{D}^2…
A note on composition operators on the bidisc
Athanasios Beslikas
In this note we give a new sufficient condition for the boundedness of the composition operator on the Dirichlet-type space on the disc, via a two dimensional change of variables f…
A class of symbols that induce bounded composition operators for Dirichlet-type spaces on the disc
Athanasios Beslikas
In this note we study the problem of determining the holomorphic self maps of the unit disc that induce a bounded composition operator on Dirichlet-type spaces. We find a class of…
New Characterizations of -type spaces on the unit ball of
Athanasios Beslikas
We provide some new characterizations of the N(p,q,s)-type spaces on the unit ball. Specifically, we give some Holland-Walsh-type characterizations for functions on the N(p,q,s) sp…