BESOV SPACES ON DOMAINS IN Rd

Abstract

We study Besov spaces 5°(LP(Í2)), 0<p,q,a<oo,on domains Í2 in Rd . We show that there is an extension operator W which is a bounded mapping from B°(LP(Ü.)) onto B%(Lp(Rd)). This is then used to derive various properties of the Besov spaces such as interpolation theorems for a pair of B%(Lp(il)), atomic decompositions for the elements of 5°(Lp(f2)), and a description of the Besov spaces by means of spline approximation.

Cite this paper

@inproceedings{DeVore1993BESOVSO, title={BESOV SPACES ON DOMAINS IN Rd}, author={Ronald A. DeVore and Robert C. Sharpley}, year={1993} }