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Lipschitz spaces on the
surface of the unit sphere in Euclidean n-space
Harvey Charles Greenwald |
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Vol. 50 (1974), No. 1, 63–80
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Abstract |
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This paper is concerned with defining Lipschitz spaces on Σn−1, the surface of the unit sphere in Rn. The importance of this example is that Σn−1 is not a group but a symmetric space. One begins with functions in Lp(Σn−1),1 ≦ p ≦∞.Σn−1 is a symmetric space and is related in a natural way to the rotation group SO (n). One can then use the group SO (n) to define first and second differences for functions in Lp(Σn−1). Such a function is the boundary value of its Poisson integral. This enables one to work with functions which are harmonic. Differences can then be replaced by derivatives. |
Mathematical Subject Classification 2000
Primary: 46E35
Secondary: 43A85
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Milestones
Received: 28 June 1971
Revised: 5 June 1973
Published: 1 January 1974
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Authors |
| Harvey Charles Greenwald | |
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