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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
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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  • [CDS] P. Cifuentes, J. R. Dorronsoro, and J. Sueiro, Boundary tangential convergence on spaces of homogeneous type, Trans. Amer. Math. Soc. 332 (1992), 331-350. MR 92j:42019
  • [CS] A. P. Calderón and R. Scott, Sobolev type inequalities for $p>0$, Studia Math. 62 (1978), 75-92. MR 58:7057
  • [CW] R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. MR 56:6264
  • [F] G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Arkiv f. Math. 13 (1975), 161-207. MR 58:13215
  • [GV] A. E. Gatto and S. Vági, Fractional integrals on spaces of homogeneous type, in Analysis and Partial Differential Equations, Cora Sadosky, editor, Marcel Dekker, New York and Basel, 1990. MR 91e:42032
  • [MS] R. Macías and C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. Math. 33 (1979), 257-270. MR 81c:32017a
  • [NRS] A. Nagel, W. Rudin, and J. Shapiro, Tangential boundary behavior of functions in Dirichlet type spaces, Ann. of Math. 116 (1982), 331-360. MR 84a:31002
  • [S] E. M. Stein, Harmonic analysis, real-variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton, NJ, 1993. MR 95c:42002

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Additional Information

A. Eduardo Gatto
Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614-3504

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

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