Lipschitz Spaces of Distributions on the Surface of Unit Sphere in Euclidean n-Space

Harvey Greenwald, California Polytechnic State University - San Luis Obispo

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Published by Pacific Journal of Mathematics, Volume 70, Issue 1, pp. 163-176. Publisher website: http://pjm.math.berkeley.edu/pjm/about/journal/cover.html

Abstract

In this paper Lipschitz spaces of distributions are defined and various inclusion relations are shown. Certain properties such as completeness, separability, and the density of the testing space for appropriate Lipschitz spaces are proved. The Littlewood-Paley function is defined and used to prove inclusion relationships between Lipschitz and Lebesgue spaces.