arXiv subjects

A. Ersin Üreyen

Publications and source records attributed to A. Ersin Üreyen.

3 recordsLinked to original sources

arXiv2026

$\mathcal H$-Harmonic Bergman-Besov Spaces on the Real Hyperbolic Ball

Using characterizations in terms of various differential operators, including partial, normal, and tangential derivatives, we extend the family of Bergman spaces of $\mathcal H$-harmonic functions on the real hyperbolic ball from the range $α>-1$ to all $α\in\mathbb R$. We then generalize several properties of Bergman spaces; projection, duality, atomic decomposition, and inclusion relations, to this extended family.

math.CV↗

arXiv2022

$\mathcal H$-Harmonic Bergman Projection on the Hyperbolic Ball

We determine precisely when the Bergman projection $P_β$ is bound\-ed from Lebesgue spaces $L^p_α$ to weighted Bergman spaces $\mathcal B^p_α$ of $\mathcal H$-harmonic functions on the hyperbolic ball, and verify a recent conjecture of M. Stoll. We obtain upper estimates for the reproducing kernel of the $\mathcal H$-harmonic Bergman space $\mathcal B^2_α$ and its partial derivatives. We also consider the projection from $L^\infty$ to the Bloch space $\mathcal B$ of $\mathcal H$-harmonic functions.

math.CV↗

arXiv2015

Graph-Directed Sprays and Their Tube Volumes via Functional Equations

The notion of sprays introduced by Lapidus and his co-workers has proved useful in the context of fractal tube formulas. In the present note, we propose a more general concept of sprays, where we allow several generators to make them more convenient for applications to graph-directed fractals. Using a simple functional equation satisfied by the volume of the inner $\varepsilon$-neighborhood of such a generalized spray, we establish a tube formula for them.

math.MG↗