Sobolev Embedding Theorems and Generalizations for Functions on a Metric Measure Space

Сибирский математический журнал

N. N. RomanovskiÄ­¹ 

[1] Sobolev Institute of Mathematics

关键词: Sobolev classes;    metric measure space;    embedding theorems;    Gagliardo–Nirenberg inequalities;   

DOI  :  10.1134/S0037446618010147

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

Considering the metric case, we define an analog of the Sobolev space of functions with generalized derivatives of order greater than 1. The space of functions with fractional generalized derivatives is also treated. We prove generalizations of the Sobolev embedding theorems and Gagliardo–Nirenberg interpolation inequalities to the metric case.

【 授权许可】

CC BY