Characterization of spaces of multipliers for Bessel potential spaces

The spaces of multipliers from a Bessel potential space with positive index of smoothness into a Bessel potential space with negative index of smoothness are considered. A description of multipliers from the space H k p (ℝn) into the space H −k p′ (ℝn) and from the space H k p (ℝn)) into the space H −l p′ (ℝn) is obtained in terms of uniformly localized Bessel potential spaces H s r,unif (ℝn).