JournalszaaVol. 28 , No. 1DOI 10.4171/zaa/1373

Description of Pointwise Multipliers in Pairs of Besov Spaces <em>B<sub>1</sub><sup>k</sup>(ℝ<sup>n</sup>)</em>

  • Tatyana Shaposhnikova

    Linköping University, Sweden
Description of Pointwise Multipliers in Pairs of Besov Spaces <em>B<sub>1</sub><sup>k</sup>(ℝ<sup>n</sup>)</em> cover

Abstract

Necessary and sufficient conditions for a function to be a multiplier mapping the Besov space B1m(Rn)B_1^m(\mathbb R^n) into the Besov space B1l(Rn)B_1^l(\mathbb R^n) with integer ll and mm, 0<lm0<l\leq m, are found. It is shown that multipliers between B1m(Rn)B_1^m(\mathbb R^n) and B1l(Rn)B_1^l(\mathbb R^n) form the space of traces of multipliers between the Sobolev classes W1m+1(R+n+1)W_1^{m+1}(\mathbb R^{n+1}_+) and W1l+1(R+n+1)W_1^{l+1}(\mathbb R^{n+1}_+).