CHARACTERIZATION OF THE MULTIPLIERS FROM Ḣr TO Ḣ-r

Title & Authors
CHARACTERIZATION OF THE MULTIPLIERS FROM Ḣr TO Ḣ-r

Abstract
In this paper, we will provide an alternative proof to characterize the pointwise multipliers which maps a Sobolev space $\small{\dot{H}^r(\mathb{R}^d)}$ to its dual $\small{\dot{H}^{-r}(\mathb{R}^d)}$ in the case 0 < $\small{r}$ < $\small{\frac{d}{2}}$ 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;
Language
English
Cited by
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