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 \r\nk\r\np (ℝn) into the space H \r\n−k\r\np′ (ℝn) and from the space H \r\nk\r\np (ℝn)) into the space H \r\n−l\r\np′ (ℝn) is obtained in terms of uniformly localized Bessel potential spaces H \r\ns\r\nr,unif (ℝn).