Description of Pointwise Multipliers in Pairs of Besov Spaces <em>B₁^k(ℝⁿ)</em>

Abstract

Necessary and sufficient conditions for a function to be a multiplier mapping the Besov space $B_1^m(\mathbb R^n)$ into the Besov space $B_1^l(\mathbb R^n)$ with integer $l$ and $m$, $0<l\leq m$, are found. It is shown that multipliers between $B_1^m(\mathbb R^n)$ and $B_1^l(\mathbb R^n)$ form the space of traces of multipliers between the Sobolev classes $W_1^{m+1}(\mathbb R^{n+1}_+)$ and $W_1^{l+1}(\mathbb R^{n+1}_+)$.