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The Modulus of Continuity of a Measure with Finite Energy

The Modulus of Continuity of a Measure with Finite Energy A general class of energy integrals in ℝn, including standard Riesz and Bessel α-energy integrals, is considered and it is shown that the modulus of continuity of positive measures for which such integrals are finite satisfy certain weighted integrability conditions. These results are deduced from an equivalent formulation of the finite energy condition in terms of related positive harmonic functions in $R^{n+1}_{+}$ . It is also shown that some of the results obtained are sharp. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

The Modulus of Continuity of a Measure with Finite Energy

Computational Methods and Function Theory , Volume 8 (1) – Mar 27, 2007

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Publisher
Springer Journals
Copyright
Copyright © 2008 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321669
Publisher site
See Article on Publisher Site

Abstract

A general class of energy integrals in ℝn, including standard Riesz and Bessel α-energy integrals, is considered and it is shown that the modulus of continuity of positive measures for which such integrals are finite satisfy certain weighted integrability conditions. These results are deduced from an equivalent formulation of the finite energy condition in terms of related positive harmonic functions in $R^{n+1}_{+}$ . It is also shown that some of the results obtained are sharp.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 27, 2007

References