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Characterization of lipschitz spaces on compact Lie groups

Part of: Approximations and expansions Abstract harmonic analysis Lie groups

Published online by Cambridge University Press:  09 April 2009

Dashan Fan  and
Zengfu Xu
Dashan Fan
Affiliation:
Department of Mathematical Sciences, University of Wisconsin, PO Box 413, Milwaukee, WI 53201, USA
Zengfu Xu
Affiliation:
Mathematics-MPS, Murdoch University, Murdoch, WA 6150, Australia
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Abstract

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Lipschitz spaces are important function spaces with relations to Hp spaces and Campanato spaces, the other two important function spaces in harmonic analysis. In this paper we give some characterizations for Lipschitz spaces on compact Lie groups, which are analogues of results in Euclidean spaces.

MSC classification

Secondary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 22E30: Analysis on real and complex Lie groups 41A25: Rate of convergence, degree of approximation 41A30: Approximation by other special function classes
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 58 , Issue 2 , April 1995 , pp. 200 - 209
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Fan, D., Hardy spaces on compact Lie groups (PhD thesis, Washington University, St. Louis, 1990).Google Scholar
[2]Krantz, S. G., ‘Structure and interpolation theorems for certain Lipschitz spaces and estimates for the ∂ equation’, Duke Math. J. 43 (1976), 417–439.Google Scholar
[3]Frazier, M., Jawerth, B. and Weiss, G., ‘Littlewood-Paley theory and the study of function spaces’, CBMS Regional Conf. Ser. in Math. 79 (Conf. Board Math. Sci, Washington D.C).Google Scholar
[4]Stein, E. M., Singular integrals and differentiability properties of functions (Princeton University Press, Princeton, 1970).Google Scholar
[5]Varadarajan, V. S., Lie groups, Lie algebras and their representations (Springer, Berlin, 1984).Google Scholar