The Singularity of Orbital Measures on Compact Lie Groups
Kathryn E. Hare and Wai Ling Yee
Source: Rev. Mat. Iberoamericana Volume 20, Number 2
(2004), 517-530.
Abstract
We find the minimal real number $k$ such that the $k$th power of the Fourier transform of any continuous, orbital measure on a classical, compact Lie group belongs to $l^{2}$. This results from an investigation of the pointwise behaviour of characters on these groups. An application is given to the study of $L^{p}$-improving measures.
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Permanent link to this document: http://projecteuclid.org/euclid.rmi/1087482025
Zentralblatt MATH identifier: 02110197
Mathematical Reviews number (MathSciNet): MR2073130
References
Bröcker, T. and Dieck, T.: Representations of compact Lie groups. Graduate Texts in Mathematics 98. Springer-Verlag, New York, 1985.
Mathematical Reviews (MathSciNet): MR781344
Hare, K. E.: The size of characters of compact Lie groups. Studia Math. 129 (1998), 1-18.
Mathematical Reviews (MathSciNet): MR1611918
Hare, K. E., Wilson, D. and Yee, W. L.: Pointwise estimates of the size of characters of compact Lie groups. J. Austral. Math. Soc. Ser. A. 69 (2000), 61-84.
Mathematical Reviews (MathSciNet): MR1767393
Humphreys, J. E.: Introduction to Lie algebras and representation theory. Graduate Texts in Mathematics 9. Springer-Verlag, New York-Berlin, 1972.
Mathematical Reviews (MathSciNet): MR499562
Ragozin, D. L.: Central measures on compact simple Lie groups. J. Functional Analysis 10 (1972), 212-229.
Mathematical Reviews (MathSciNet): MR340965
Digital Object Identifier: doi:10.1016/0022-1236(72)90050-X
Zentralblatt MATH: 0286.43002
Ricci, F. and Stein, E. M.: Harmonic analysis on nilpotent groups and singular integrals. III. Fractional integration along manifolds. J. Funct. Anal. 86 (1989), 360-389.
Mathematical Reviews (MathSciNet): MR1021141
Digital Object Identifier: doi:10.1016/0022-1236(89)90057-8
Zentralblatt MATH: 0684.22006
Ricci, F. and Travaglini, G.: $L^p-L^q$ estimates for orbital measures and Radon transform on compact Lie groups and Lie algebras. J. Funct. Anal. 129 (1995), 132-147.
Mathematical Reviews (MathSciNet): MR1322645
Digital Object Identifier: doi:10.1006/jfan.1995.1045
Zentralblatt MATH: 0843.43011
Stein, E. M. and Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton Mathematical Series 32. Princeton University Press, Princeton, N.J., 1971.
Mathematical Reviews (MathSciNet): MR304972
Varadarajan, V. S.: Lie groups, Lie algebras, and their representations. Reprint of the 1974 edition. Graduate Texts in Mathematics 102. Springer-Verlag, New York, 1984.
Mathematical Reviews (MathSciNet): MR746308
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