Multipliers in spaces of Bessel potentials: The case of indices of nonnegative smoothness.

The aim of the paper is to study spaces of multipliers acting from the Bessel potential space H (ℝ) to the other Bessel potential space H (ℝ). We obtain conditions ensuring the equivalence of uniform and standard multiplier norms on the space of multipliers In the case , the space M[ H (ℝ) → H (ℝ) can be described explicitly. Namely, we prove in this paper that the latter space coincides with the space H (ℝ) of uniformly localized Bessel potentials introduced by Strichartz. It is also proved that if both smoothness indices s and t are nonnegative, then such a description is possible only for the given values of the indices. [ABSTRACT FROM AUTHOR]