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Multipliers Between Sobolev Spaces

Published online by Cambridge University Press:  20 November 2018

R. C. Fabec
R. C. Fabec*
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana, USA 70803
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Abstract

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A sufficient condition for the boundedness of a multiplier from a Sobolev space of index t > 1 / 4 to one of opposite index — t is obtained. The condition relates the indices of the Sobolev spaces to which the multiplier belongs to the pairs of Sobolev spaces between which the multiplier is bounded. The result is applied to homogeneous multipliers and a description of these multipliers in this setting is presesented. Extensions to higher dimensions are indicated.

Keywords

42B1546E35
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 4 , 01 December 1991 , pp. 465 - 473
Copyright
Copyright © Canadian Mathematical Society 1991

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