Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774969 | Journal of Mathematical Analysis and Applications | 2017 | 24 Pages |
Abstract
In this paper, we obtain the Franke-Jawerth embedding property of HajÅasz-Besov and HajÅasz-Triebel-Lizorkin spaces on a measure metric space (X,d,μ) which is Ahlfors regular with dimension “Q”. As applications, we show that, when (X,d,μ) is doubling and satisfies an Ahlfors lower bound condition with Q, then the HajÅasz-Besov space Np,qs(X) with pâ(Q,â], sâ(Qp,1] and qâ(0,â] and the HajÅasz-Triebel-Lizorkin space Mp,qs(X) with pâ(Q,â), sâ(Qp,1] and qâ(QQ+s,â] are algebras under pointwise multiplication and, moreover, when X is Ahlfors Q-regular, we characterize the class of all pointwise multipliers on the HajÅasz-Triebel-Lizorkin space Mp,qs(X) for pâ(Q,â), sâ(Qp,1] and qâ(QQ+s,â] by its related uniform space.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Wen Yuan,