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Lipschitz Spaces on the Surface of Unit Sphere in Euclidean n-Space
Pacific Journal of Mathematics
  • Harvey Greenwald, California Polytechnic State University - San Luis Obispo
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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.

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Citation Information
Harvey Greenwald. "Lipschitz Spaces on the Surface of Unit Sphere in Euclidean n-Space" Pacific Journal of Mathematics Vol. 50 Iss. 1 (1974) p. 63 - 80
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