Vol. 50, No. 1, 1974

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Lipschitz spaces on the surface of the unit sphere in Euclidean n-space

Harvey Charles Greenwald

Vol. 50 (1974), No. 1, 63–80

This paper is concerned with defining Lipschitz spaces on Σn1, the surface of the unit sphere in Rn. The importance of this example is that Σn1 is not a group but a symmetric space. One begins with functions in Lpn1),1 p .Σn1 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 Lpn1). 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
Received: 28 June 1971
Revised: 5 June 1973
Published: 1 January 1974
Harvey Charles Greenwald