Affiliation:
1. School of Mathematics and Statistics Southwest University Chongqing China
2. School of Mathematical Sciences Zhejiang Normal University Jinhua Zhejiang China
Abstract
AbstractIn this note, we study a nonlocal version of the Sobolev inequality
where is the best constant, * denotes the standard convolution and denotes the classical Sobolev space with respect to the norm . By using the nondegeneracy property of the extremal functions, we prove that the existence of the gradient type remainder term and a reminder term in the weak ‐norm of above inequality for all with .
Funder
Natural Science Foundation of Zhejiang Province
National Natural Science Foundation of China