A note on homogeneous Sobolev spaces of fractional order

被引：30
|
作者：
Brasco, Lorenzo [1 ]
Salort, Ariel [2 ,3 ]
机构：
[1] Univ Ferrara, Dipartimento Matemat & Informat, Via Machiavelli 35, I-44121 Ferrara, Italy
[2] Univ Buenos Aires, FCEN, Dept Matemat, Buenos Aires, DF, Argentina
[3] Consejo Nacl Invest Cient & Tecn, IMAS, Buenos Aires, DF, Argentina
来源：
ANNALI DI MATEMATICA PURA ED APPLICATA | 2019年 / 198卷 / 04期
关键词：
Nonlocal operators; Fractional Sobolev spaces; Real interpolation; Poincare inequality;
D O I：
10.1007/s10231-018-0817-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a homogeneous fractional Sobolev space obtained by completion of the space of smooth test functions, with respect to a Sobolev-Slobodecki norm. We compare it to the fractional Sobolev space obtained by the K-method in real interpolation theory. We show that the two spaces do not always coincide and give some sufficient conditions on the open sets for this to happen. We also highlight some unnatural behaviors of the interpolation space. The treatment is as self-contained as possible.
引用
收藏
页码：1295 / 1330
页数：36
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