T. Ferguson

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20152020

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math.CV2019

Bergman and Szego projections, Extremal Problems, and Square Functions

Timothy Ferguson

We study estimates for Hardy space norms of analytic projections. We first find a sufficient condition for the Bergman projection of a function in the unit disc to belong to the Ha…

math.CV2018

Equivalence among various variable exponent Hardy or Bergman spaces

Timothy Ferguson

We study the question of when two weighted variable exponent Bergman spaces or Hardy spaces are equivalent. As an application, we show that variable exponent Hardy spaces have a cl…

math.CV2018

Sums of Weighted Differentiation Composition Operators

Soumyadip Acharyya, Timothy Ferguson

We solve an interpolation problem in $A_{α}^{p}$ involving specifying a set of (possibly not distinct) $n$ points, where the $k^{th}$ derivative at the $k^{th}$ point…

math.CV2017

Uniform Approximation of Extremal Functions in Weighted Bergman Spaces

Timothy Ferguson

We discuss approximation of extremal functions by polynomials in the weighted Bergman spaces $A_{α}^{p}$ where $- 1 < α < 0$ and $- 1 < α < p - 2$ . We obtain bounds on how close the approxim…

math.CV2017

Bounds on the Norm of the Backward Shift and Related Operators in Hardy and Bergman Spaces

Timothy Ferguson

We study bounds for the backward shift operator $f \mapsto (f (z) - f (0)) / z$ and the related operator $f \mapsto f - f (0)$ on Hardy and Bergman spaces of analytic and harmonic functio…

math.CV2015

Extremal Problems in Bergman Spaces and an Extension of Ryabykh's $H^{p}$ Regularity Theorem For $1 < p < \infty$

Timothy Ferguson

We study linear extremal problems in the Bergman space $A^{p}$ of the unit disc, where $1 < p < \infty$ . Given a functional on the dual space of $A^{p}$ with representing kernel $k \in…

Bergman and Szego projections, Extremal Problems, and Square Functions

Equivalence among various variable exponent Hardy or Bergman spaces

Sums of Weighted Differentiation Composition Operators

Uniform Approximation of Extremal Functions in Weighted Bergman Spaces

Bounds on the Norm of the Backward Shift and Related Operators in Hardy and Bergman Spaces

Extremal Problems in Bergman Spaces and an Extension of Ryabykh's Hp Regularity Theorem For 1<p<∞

Extremal Problems in Bergman Spaces and an Extension of Ryabykh's $H^{p}$ Regularity Theorem For $1 < p < \infty$