Pointwise multipliers of Besov spaces of smoothness zero and spaces of continuous functions

Abstract

We characterize the set of pointwise multipliers of the Besov spaces $B_{\infty ,1}^0$ and $B_{\infty ,\infty }^0$ . These characterizations are used to obtain regularity results for elliptic partial differential equations. In addition several counterexamples are provided and the relation of various spaces of continuous functions to these multiplier classes are studied.