5 papers · 1 filter
A property of boundary extensions of atomic singular inner functions
Iason Efraimidis, Adrian Llinares, Sullivan MacDonald +2
Using a property of the Hilbert transform, we prove a measure theoretic result concerning the extensions of atomic singular inner functions to the circle. Various alternative proof…
Truncated Dirichlet estimates for Bloch functions
Iason Efraimidis, Adrián Llinares, Alejandro Mas
We study the truncated Dirichlet functional \[ Φ_n (f) = \sum_{k = 1}^n k |a_k|^2, \quad f(z) = \sum_{k = 0}^\infty a_k z^k, \] when belongs to the Bloch space. If ,…
The norm of the backward shift on is
Konstantinos Bampouras, Adrián Llinares
We prove that the backward shift operator on has norm equal to , with . Furthermore, we characterize all extremal functions; they are pr…
classes in the Dirichlet range: inner-outer factorization, Carleson measures and weak products
Alberto Dayan, Adrián Llinares, Miguel Monsalve-López
We study properties of spaces in the Dirichlet range, recently defined by Brevig, Kulikov, Seip and Zlotnikov as the set of all holomorphic functions on the unit disc $\mat…
On the convolution of convex 2-gons
Martin Chuaqui, Rodrigo Hernández, Adrián Llinares +1
We study the convolution of functions of the form \[ f_α(z) := \dfrac{\left( \frac{1 + z}{1 - z} \right)^α- 1}{2 α}, \] which map the open unit disk of the complex plane onto polyg…