Integral Equations and Operator Theory

, Volume 42, Issue 2, pp 174–182

Marcinkiewicz integral on hardy spaces

  • Yong Ding
  • Shanzhen Lu
  • Quigying Xue
Article

Abstract

In this paper we prove that the Marcinkiewicz integral μΩ is an operator of type (H1,L1) and of type (H1,∞,L1,∞). As a corollary of the results above, we obtain again the the weak type (1,1) boundedness of μΩ, but the smoothness condition assumed on Ω is weaker than Stein's condition.

2000 Mathematics Subject Classification

42B25 42B30 

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Copyright information

© Birkhäuser Verlag 2002

Authors and Affiliations

  • Yong Ding
    • 1
  • Shanzhen Lu
    • 1
  • Quigying Xue
    • 1
  1. 1.Department of MathematicsBeijing Normal UniversityBeijingP.R. of China

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