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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On functions arising as potentials
on spaces of homogeneous type


Authors: A. Eduardo Gatto and Stephen Vági
Journal: Proc. Amer. Math. Soc. 125 (1997), 1149-1152
MSC (1991): Primary 42C99, 26A33, 44A99; Secondary 31C15
DOI: https://doi.org/10.1090/S0002-9939-97-03764-7
MathSciNet review: 1372029
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Abstract: On a space of homogeneous type we consider functions $F$ in $L^p$, $1<p<\infty $, which are potentials of order $\alpha $ of $L^p$ functions. We show that these functions belong to the class of smooth functions $C^{p,\alpha }$ of Calderón-Scott. This result has applications to tangential convergence.


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Additional Information

A. Eduardo Gatto
Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614-3504
Email: aegatto@condor.depaul.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03764-7
Received by editor(s): October 25, 1995
Received by editor(s) in revised form: January 25, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1997 American Mathematical Society