Computational Methods and Function Theory 8 (2008), No. 1, 47--56
Copyright Heldermann Verlag 2008
J. Brian Twomey
twomeyjb@ucc.ie , University College Cork, Mathematics Department, Ireland.
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 Rn+1+. It is also shown that some of the results obtained are sharp.
Keywords: Energy integrals, finite measures, modulus of continuity, positive harmonic functions.
MSC 2000: Primary 31A05; Secondary 28A12.
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