Radial Variation of Positive Harmonic Functions and Bloch Functions

Katharina Riegler

Radial Variation of Positive Harmonic Functions and Bloch Functions

Katharina Riegler

Department of Functional Analysis

Research output: Thesis › Doctoral thesis

Abstract

In this thesis two topics are treated. First, we provide variational estimates for Bloch functions on the unit ball of R d extending previous work on the Anderson conjecture for conformal maps on the unit disc. The second part presents the necessary modifications of the proof by Mozolyako and Havin on the variation of positive harmonic functions to work for Lipschitz domains instead of C 2 domains.

Original language	English
Supervisors/Reviewers	Müller, Paul, Supervisor
Place of Publication	Linz
Publisher	Johannes Kepler Universität
Publication status	Published - 2020

Fields of science

101002 Analysis
101032 Functional analysis

JKU Focus areas

Digital Transformation

Cite this

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title = "Radial Variation of Positive Harmonic Functions and Bloch Functions",

abstract = "In this thesis two topics are treated. First, we provide variational estimates for Bloch functions on the unit ball of R d extending previous work on the Anderson conjecture for conformal maps on the unit disc. The second part presents the necessary modifications of the proof by Mozolyako and Havin on the variation of positive harmonic functions to work for Lipschitz domains instead of C 2 domains.",

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TY - BOOK

T1 - Radial Variation of Positive Harmonic Functions and Bloch Functions

AU - Riegler, Katharina

PY - 2020

Y1 - 2020

N2 - In this thesis two topics are treated. First, we provide variational estimates for Bloch functions on the unit ball of R d extending previous work on the Anderson conjecture for conformal maps on the unit disc. The second part presents the necessary modifications of the proof by Mozolyako and Havin on the variation of positive harmonic functions to work for Lipschitz domains instead of C 2 domains.

AB - In this thesis two topics are treated. First, we provide variational estimates for Bloch functions on the unit ball of R d extending previous work on the Anderson conjecture for conformal maps on the unit disc. The second part presents the necessary modifications of the proof by Mozolyako and Havin on the variation of positive harmonic functions to work for Lipschitz domains instead of C 2 domains.

UR - https://epub.jku.at/urn:nbn:at:at-ubl:1-35296

M3 - Doctoral thesis

PB - Johannes Kepler Universität

CY - Linz

ER -

Radial Variation of Positive Harmonic Functions and Bloch Functions

Abstract

Fields of science

JKU Focus areas

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