Isoperimetric Inequalities for Bergman Analytic Content

Gardiner, Stephen J.; Ghergu, Marius; Sjödin, Tomas

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Isoperimetric Inequalities for Bergman Analytic Content

Gardiner, Stephen J.

Univ Coll Dublin, Ireland.

Ghergu, Marius

Univ Coll Dublin, Ireland.

Sjödin, Tomas

Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.

2020 (English)In: Indiana University Mathematics Journal, ISSN 0022-2518, E-ISSN 1943-5258, Vol. 69, no 4, p. 1231-1249Article in journal (Refereed) Published

Abstract [en]

The Bergman p-analytic content (1 <= p < infinity) of a planar domain Omega measures the L-p (Omega)-distance between (z) over bar and the Bergman space A(p) (Omega) of holomorphic functions. It has a natural analogue in all dimensions which is formulated in terms of harmonic vector fields. This paper investigates isoperimetric inequalities for Bergman p-analytic content in terms of the St. Venant functional for torsional rigidity, and addresses the cases of equality with the upper and lower bounds.

Place, publisher, year, edition, pages

INDIANA UNIV MATH JOURNAL , 2020. Vol. 69, no 4, p. 1231-1249

Keywords [en]

Harmonic vector field; Bergman space; isoperimetric inequality; torsional rigidity

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Mathematical Analysis

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URN: urn:nbn:se:liu:diva-168197DOI: 10.1512/iumj.2020.69.7898ISI: 000546916200006OAI: oai:DiVA.org:liu-168197DiVA, id: diva2:1460227

Available from: 2020-08-22 Created: 2020-08-22 Last updated: 2020-08-22

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Gardiner, Stephen J.

Ghergu, Marius

Sjödin, Tomas

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