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Bilinear forms on non-homogeneous Sobolev spaces

  • Carme Cascante EMAIL logo and Joaquín M. Ortega
From the journal Forum Mathematicum

Abstract

In this paper, we show that if bL2(n), then the bilinear form defined on the product of the non-homogeneous Sobolev spaces Hs2(n)×Hs2(n), 0<s<1, by

(f,g)Hs2(n)×Hs2(n)n(Id-Δ)s2(fg)(𝐱)b(𝐱)d𝐱

is continuous if and only if the positive measure |b(𝐱)|2d𝐱 is a trace measure for Hs2(n).


Communicated by Christopher D. Sogge


Award Identifier / Grant number: MTM2017-83499-P

Award Identifier / Grant number: MTM2015-69323-REDT

Award Identifier / Grant number: MDM-2014-0445

Funding source: Generalitat de Catalunya

Award Identifier / Grant number: 2017SGR358

Funding statement: The research was supported in part by Ministerio de Economía y Competitividad, Spain, projects MTM2017-83499-P and MTM2015-69323-REDT, and Generalitat de Catalunya, project 2017SGR358. The first author was also supported in part by Ministerio de Economía y Competitividad, Spain, project MDM-2014-0445.

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Received: 2019-11-07
Revised: 2020-03-18
Published Online: 2020-04-15
Published in Print: 2020-07-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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