Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2012.04.13
  • Published : 2013.05.31
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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.

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References

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