A Sobolev non embedding

• DOI: 10.4171/rlm/707
• Publication Date: 2015-06-11T21:45:05Z
• Authors: Petru Mironescu; Winfried Sickel
• Keywords: MSC 46E35; Sobolev and Slobodeskii spaces; 0101 mathematics; [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]; wavelets; lacunary series; embeddings; 01 natural sciences; 510; 620

If

\Omega

is a bounded domain in

\mathbb R^n

,

1 ≤ q < p ≤ \infty

and

s=0, 1, 2,\ldots

, then we clearly have

W^{s,p}(\Omega)\subset W^{s,q}(\Omega)

. We prove that this property does not hold when

s

in not an integer.