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Harmonic and Superharmonic Majorants on the Disk
Author(s) -
Borichev Alexander,
Nicolau Artur,
Thomas Pascal J.
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609306018339
Subject(s) - subharmonic function , mathematics , harmonic , unit disk , mathematical analysis , envelope (radar) , lipschitz continuity , pure mathematics , acoustics , physics , computer science , telecommunications , radar
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. 2000 Mathematics Subject Classification 31A05.