Journal title
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
DOI
10.1007/s00526-021-01934-6
Issue
2
Volume
60
Last updated
2023-08-28T14:15:08.08+01:00
Abstract
© 2021, The Author(s). Our aim is to characterize the homogeneous fractional Sobolev–Slobodeckiĭ spaces Ds,p(Rn) and their embeddings, for s∈ (0 , 1] and p≥ 1. They are defined as the completion of the set of smooth and compactly supported test functions with respect to the Gagliardo–Slobodeckiĭ seminorms. For sp<n or s= p= n= 1 we show that Ds,p(Rn) is isomorphic to a suitable function space, whereas for sp≥n it is isomorphic to a space of equivalence classes of functions, differing by an additive constant. As one of our main tools, we present a Morrey–Campanato inequality where the Gagliardo–Slobodeckiĭ seminorm controls from above a suitable Campanato seminorm.
Symplectic ID
1137536
Submitted to ORA
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Publication type
Journal Article
Publication date
01 Apr 2021