《数学学报》英文版Vol．23(2007),No．4论文摘要(英文)

Parametrized Area Integrals on Hardy Spaces and Weak Hardy Spaces Yong DING Shan Zhen LU Qing Ying XUE In this paper,the authors prove that ifΩsatisfies a class of thc integral Dini condition,then the parametrized area integralμ_(Ω,S)~ρis a bounded operator from the Hardy space H^1(R^n)to L^1(R^n)and from the weak Hardy space H^(1,∞)(R^n)to L^(1,∞)(R^n),respectively.As corollaries of the above results,it is shown thatμ_(Ω,S)~ρis also an operator of weak type(1,1)and of type(p,p)for 1<p<2,respectively.These conclusions are substantial improvement and extension of some known results.