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Acta Mathematica Sinica

, Volume 13, Issue 1, pp 45–58 | Cite as

Some characterizations of weighted Herz-type Hardy spaces and their applications

  • Lu Shanzhen
  • Yang Dachun
Article

Abstract

In this paper, the authors first establish some new real-variable characterizations of Herz-type Hardy spaces\(H \mathop {K _q^{\alpha ,p} }\limits^ \bullet (\omega _1 ;\omega _2 )\) and\(H K_q^{\alpha ,p} (\omega _1 ;\omega _2 )\), where ω13 ∈ A1-weight, 1<q>∞,n(1−1/q)≤α<∞ and 0<p<∞. Then, using these new characterizations, they investigate the convergence of a bounded set in these spaces, and study the boundedness of some potential operators on these spaces.

Keywords

Herz space Herz-type Hardy space Potential operator 

1991 MR Subject Classification

42B30 

Chinese Library Classification

O174.2 

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Copyright information

© Institute of Mathematics, Academia Sinica 1996

Authors and Affiliations

  • Lu Shanzhen
    • 1
  • Yang Dachun
    • 1
  1. 1.Department of MathematicsBeijing Normal UniversityBeijingChina

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