Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications

• Autorzy: Xiaming Chen , Renjin Jiang , Dachun Yang
• Języki publikacji: EN

Abstrakty

EN

Let Ω ⊂ Rn be a strongly Lipschitz domain. In this article, the authors study Hardy spaces, Hpr (Ω)and Hpz (Ω), and Hardy-Sobolev spaces, H1,pr (Ω) and H1,pz,0 (Ω) on , for p ∈ ( n/n+1, 1]. The authors establish grand maximal function characterizations of these spaces. As applications, the authors obtain some div-curl lemmas in these settings and, when is a bounded Lipschitz domain, the authors prove that the divergence equation div u = f for f ∈ Hpz (Ω) is solvable in H1,pz,0 (Ω) with suitable regularity estimates.

Słowa kluczowe

EN

Hardy space; Hardy-Sobolev space; grand maximal function; div-curl formula; divergence equation

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2016
• Tom: 4
• Numer: 1

Daty

otrzymano

2016-11-08

zaakceptowano

2016-12-19

online

2016-12-30

Twórcy

autor

Xiaming Chen

• School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China

autor

Renjin Jiang

• Center for Applied Mathematics, Tianjin University, Tianjin 300072, China and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

autor

Dachun Yang

• School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China

Identyfikatory

DOI

10.1515/agms-2016-0017