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A. Ersin Ureyen

Publications and source records attributed to A. Ersin Ureyen.

4 recordsLinked to original sources
arXiv2023

Harmonic Bloch Space on the Real Hyperbolic Ball

We study the Bloch and the little Bloch spaces of harmonic functions on the real hyperbolic ball. We show that the Bergman projections from $L^\infty(\mathbb B)$ to $\mathcal B$, and from $C_0(\mathbb B)$ to $\mathcal B_0$ are onto. We verify that the dual space of the hyperbolic harmonic Bergman space $\mathcal B^1_α$ is $\mathcal B$ and its predual is $\mathcal B_0$. Finally, we obtain an atomic decomposition of Bloch functions as a series of Bergman reproducing kernels.

math.CV↗
arXiv2023

Harmonic Bergman Spaces on the Real Hyperbolic Ball: Atomic Decomposition, Interpolation and Inclusion Relations

For $α>-1$ and $0<p<\infty$, we study weighted Bergman spaces $\mathcal B^p_α$ of harmonic functions on the real hyperbolic ball and obtain an atomic decomposition of these spaces in terms of reproducing kernels. We show that an $r$-separated sequence $\{a_m\}$ with sufficiently large $r$ is an interpolating sequence for $\mathcal B^p_α$. Using these we determine precisely when a Bergman space $\mathcal B^p_α$ is included in another Bergman space $\mathcal B^q_β$.

math.CV↗
arXiv2010

On the Minkowski Measurability of Self-Similar Fractals in R^d

M. Lapidus and C. Pomerance (1990-1993) and K.J. Falconer (1995) proved that a self-similar fractal in $\mathbb{R}$ is Minkowski-measurable iff it is of non-lattice type. D. Gatzouras (1999) proved that a self-similar fractal in $\mathbb{R}^d$ is Minkowski measurable if it is of non-lattice type (though the actual computation of the content is intractable with his approach) and conjectured that it is not Minkowski measurable if it is of lattice type. Under mild conditions we prove this conjecture and in the non-lattice case we improve his result in the sense that we express the content of the fractal in terms of the residue of the associated $ζ$-function at the Minkowski-dimension.

math.MG↗