S. Deterding

activity

20172025

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math.CV2025

Geometric conditions for bounded point evaluations in several complex variables

Stephen Deterding

Let $U$ be a bounded domain in $C^{d}$ and let $L_{a}^{p} (U)$ , $1 \leq p < \infty$ , denote the space of functions that are analytic on $U$ and bounded in the $L^{p}$ nor…

math.CV2025

Analytic structure in spaces of Lipschitz functions

Stephen Deterding

Let $U \subseteq C$ be bounded and open. For $0 < α < 1$ , $A_{α} (U)$ is the set of functions in the little Lipschitz class with exponent $α$ that are analytic in a neighborhoo…

math.CV2024

Approximate Taylor theorem for analytic Lipschitz functions

Stephen Deterding

Let $U$ be a bounded open subset of the complex plane and let $A_{α} (U)$ denote the set of functions analytic on $U$ that also belong to the little Lipschitz class with Lipschitz exp…

math.CV2023

Bounded point derivations on Campanato spaces

Evan Abshire, Stephen Deterding

Let $X$ be a compact subset of the complex plane and $x \in X$ . A necessary and sufficient condition is given in terms of Hausdorff contents for the existence of a bounded point de…

math.CV2021

Boundary Smoothness conditions for functions in $R^{p} (X)$

Stephen Deterding

Let $X$ be a compact subset of the complex plane and let $R^{p} (X)$ , $2 < p < \infty$ , denote the closure of the rational functions with poles off $X$ in the $L^{p}$ norm. In this paper…

math.CV2019

Bounded point derivations and functions of bounded mean oscillation

Stephen Deterding

Let $X$ be a subset of the complex plane and let $A_{0} (X)$ denote the space of VMO functions that are analytic on $X$ . $A_{0} (X)$ is said to admit a bounded point derivation of order…

math.CV2018

Non-tangential limits for analytic Lipschitz functions

Stephen Deterding

Let $U$ be a bounded open subset of the complex plane. Let $0 < α < 1$ and let $A_{α} (U)$ denote the space of functions that satisfy a Lipschitz condition with exponent $α$ on the comple…

math.CV2017

A formula for a bounded point derivation on $R^{p} (X)$

Stephen Deterding

Let $X$ be a compact subset of the complex plane. It is shown that if a point $x_{0}$ admits a bounded point derivation on $R^{p} (X)$ , the closure of rational function with poles off $…

math.CV2017

Bounded point derivations on $R^{p} (X)$ and approximate derivatives

Stephen Deterding

It is shown that if a point $x_{0}$ admits a bounded point derivation on $R^{p} (X)$ , the closure of rational function with poles off $X$ in the $L^{p} (d A)$ norm, for $p > 2$ , then there i…

Geometric conditions for bounded point evaluations in several complex variables

Analytic structure in spaces of Lipschitz functions

Approximate Taylor theorem for analytic Lipschitz functions

Bounded point derivations on Campanato spaces

Boundary Smoothness conditions for functions in Rp(X)

Bounded point derivations and functions of bounded mean oscillation

Non-tangential limits for analytic Lipschitz functions

A formula for a bounded point derivation on Rp(X)

Bounded point derivations on Rp(X) and approximate derivatives

Boundary Smoothness conditions for functions in $R^{p} (X)$

A formula for a bounded point derivation on $R^{p} (X)$

Bounded point derivations on $R^{p} (X)$ and approximate derivatives