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http://dx.doi.org/10.4134/BKMS.2013.50.3.915

CHARACTERIZATION OF THE MULTIPLIERS FROM Ḣr TO Ḣ-r  

Gala, Sadek (Department of Mathematics University of mostaganem)
Sawano, Yoshihiro (Department of Mathematics and Information Sciences Tokyo Metropolitan University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.3, 2013 , pp. 915-928 More about this Journal
Abstract
In this paper, we will provide an alternative proof to characterize the pointwise multipliers which maps a Sobolev space $\dot{H}^r(\mathb{R}^d)$ to its dual $\dot{H}^{-r}(\mathb{R}^d)$ in the case 0 < $r$ < $\frac{d}{2}$ by a simple application of the definition of fractional Sobolev space. The proof relies on a method introduced by Maz'ya-Verbitsky [9] to prove the same result.
Keywords
multiplier space; Sobolev space; fractional differentiation;
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