Lipschitz Spaces on the Surface of Unit Sphere in Euclidean n-SpacePacific Journal of Mathematics
AbstractThis 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.
Citation InformationHarvey 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
Available at: http://works.bepress.com/hgreenwa/3/