排序方式: 共有5条查询结果,搜索用时 15 毫秒
1
1.
2.
3.
We study Sobolev type spaces defined in terms of sharp maximal functions on Ahlfors regular subsets of and the relation between these spaces and traces of classical Sobolev spaces. 相似文献
4.
Toni Heikkinen Lizaveta Ihnatsyeva Heli Tuominen 《Journal of Fourier Analysis and Applications》2016,22(2):334-382
We show that a domain is an extension domain for a Haj?asz–Besov or for a Haj?asz–Triebel–Lizorkin space if and only if it satisfies a measure density condition. We use a modification of the Whitney extension where integral averages are replaced by median values, which allows us to handle also the case \(0<p<1\). The necessity of the measure density condition is derived from embedding theorems; in the case of Haj?asz–Besov spaces we apply an optimal Lorentz-type Sobolev embedding theorem which we prove using a new interpolation result. This interpolation theorem says that Haj?asz–Besov spaces are intermediate spaces between \(L^p\) and Haj?asz–Sobolev spaces. Our results are proved in the setting of a metric measure space, but most of them are new even in the Euclidean setting, for instance, we obtain a characterization of extension domains for classical Besov spaces \(B^s_{p,q}\), \(0<s<1\), \(0<p<\infty \), \(0<q\le \infty \), defined via the \(L^p\)-modulus of smoothness of a function. 相似文献
5.
Muckenhoupt Ap-properties of Distance Functions and Applications to Hardy–Sobolev -type Inequalities
Dyda Bartłomiej Ihnatsyeva Lizaveta Lehrbäck Juha Tuominen Heli Vähäkangas Antti V. 《Potential Analysis》2019,50(1):83-105
Potential Analysis - Let X be a metric space equipped with a doubling measure. We consider weights w(x) = dist(x,E)?α, where E is a closed set in X and $\alpha \in \mathbb {R}$ . We... 相似文献
1