On the H1-L1 boundedness of operators

被引：82

作者：

Meda, Stefano ^{[1
]}

Sjogren, Peter ^{[2
,3
]}

Vallarino, Maria ^{[4
]}

机构：

[1] Univ Milano Bicocca, Dept Math & Applicaz, I-20125 Milan, Italy

[2] Chalmers Univ Technol, Dept Math Sci, SE-41296 Gothenburg, Sweden

[3] Univ Gothenburg, Dept Math Sci, SE-41296 Gothenburg, Sweden

[4] Univ Orleans, Lab MAPMO, UMR 6628, UFR Sci, F-45067 Orleans, France

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 136卷 / 08期

关键词：

BMO; atomic Hardy space; extension of operators;

D O I：

10.1090/S0002-9939-08-09365-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that if q is in (1,infinity), Y is a Banach space, and T is a linear operator defined on the space of finite linear combinations of (1, q)-atoms in R-n with the property that sup{parallel to Ta parallel to Y : a is a (1,q)-atom} < infinity, then T admits a ( unique) continuous extension to a bounded linear operator from H-1(R-n) to Y. We show that the same is true if we replace (1,q)-atoms by continuous (1,infinity)-atoms. This is known to be false for (1,infinity)-atoms.

引用

页码：2921 / 2931

页数：11

共 17 条

[1]

[Anonymous], 1987, Topological vector classes, DOI DOI 10.1007/978-3-642-61715-7

[2] Boundedness of operators on Hardy spaces via atomic decompositions [J].