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A Whitney extension theorem in L p and Besov spaces

Alf JonssonHans Wallin — 1978

Annales de l'institut Fourier

The classical Whitney extension theorem states that every function in Lip ( β , F ) , F R n , F closed, k < β k + 1 , k a non-negative integer, can be extended to a function in Lip ( β , R n ) . Her Lip ( β , F ) stands for the class of functions which on F have continuous partial derivatives up to order k satisfying certain Lipschitz conditions in the supremum norm. We formulate and prove a similar theorem in the L p -norm. The restrictions to R d , d < n , of the Bessel potential spaces in R n and the Besov or generalized Lipschitz spaces in...

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