Multipliers from Sobolev space H^\al_p into H^-\al_p

2003/01/13 by M. I. Neiman-zade, Neiman-zade, M. I., A. A. Shkalikov +1
Mathematics · #35J10 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA #msc:35J10 #msc:46E35

paper · pdf · doi:10.48550/arxiv.math/0301121

11 pages

arxiv created 2003/01/13 · arxiv updated 2009/11/30

Abstract

A function q(x) is said to be a multiplier from the Sobolev space H^\al_p(Rⁿ) into H^-\al_p(Rⁿ) if the operator Lf(x)=q(x)f(x) is a bounded operator from the first space into the second one. Let M^\al_p the the space of such multipliers. In this paper we give the description of the spaces M^\al_p provided the condition \al>min(n/p,n/p'). In the case \al≤ min(n/p,n/p') we obtain some embedding theorems for Sobolev spaces with negative smoothness indices into M^\al_p.

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