CHARACTERIZATION OF THE MULTIPLIERS FROM Ḣ_rTO Ḣ_-r

Abstract

Abstract. In this paper, we will provide an alternative proof to characterize the pointwise multipliers which maps a Sobolev spaceR d in the case 0 < r < 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.

Improved regularity criterion for the 3D Navier–Stokes equations via the gradient of one velocity component

“…The purpose of this note is to extend the regularity criterion (1.2)-( 1.3) to the multiplier space Z α (R 3 ), which is larger than the Lebesgue space L 3 2α (R 3 ) (for details see e.g. [7]). Now our regularity criterion reads as follows.…”