Extension of Cm,a-smooth functions by linear operators

Charles Fefferman

doi:10.4171/rmi/568

Extension of C^m,a-smooth functions by linear operators

Charles Fefferman

Mathematics

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

Abstract

Let Cm,u,(Rn) be the space of functions on Rn whose mth derivatives have modulus of continuity u. For E C Rn, let Cm,tu(E) be the space of all restrictions to E of functions in Cm,u,(R11). We show that there exists a bounded linear operator T : Cm'u'(E) ≥ Cm,a,(Rn) such that, for any f S Cm,a,(E), we have Tf = f on E.

Original language	English (US)
Pages (from-to)	1-48
Number of pages	48
Journal	Revista Matematica Iberoamericana
Volume	25
Issue number	1
DOIs	https://doi.org/10.4171/rmi/568
State	Published - 2009

All Science Journal Classification (ASJC) codes

General Mathematics

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10.4171/rmi/568

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AB - Let Cm,u,(Rn) be the space of functions on Rn whose mth derivatives have modulus of continuity u. For E C Rn, let Cm,tu(E) be the space of all restrictions to E of functions in Cm,u,(R11). We show that there exists a bounded linear operator T : Cm'u'(E) ≥ Cm,a,(Rn) such that, for any f S Cm,a,(E), we have Tf = f on E.

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Extension of C^m,a-smooth functions by linear operators

Abstract

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