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HARMONIC AND SUPERHARMONIC MAJORANTS ON THE DISK

Published online by Cambridge University Press:  16 March 2006

ALEXANDER BORICHEV ,
ARTUR NICOLAU  and
PASCAL J. THOMAS
ALEXANDER BORICHEV
Affiliation:
LaBAG, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence CEDEX, [email protected]
ARTUR NICOLAU
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, [email protected]
PASCAL J. THOMAS
Affiliation:
Laboratoire de Mathématiques Emile Picard, UMR CNRS 5580, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse CEDEX, [email protected]
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Abstract

A proof is given to show that a positive function on the unit disk admits a harmonic majorant if and only if it has a certain explicit upper envelope that admits a superharmonic majorant. The (logarithmic) Lipschitz regularity of this superharmonic majorant is discussed.

Keywords

31A05
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 2 , April 2006 , pp. 250 - 260
Copyright
The London Mathematical Society 2006

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