沿旋转曲面单参数Marcinkiewicz积分算子的L^p有界性

L^p Boundedness of a Class of One-Paramter Marcinkiewicz Integral Operators Associated with Surfaces of Revolution

对沿旋转曲面的单参数Marcinkiewicz积分算子进行了研究,在积分核满足较弱的尺寸条件下建立了该算子的Lp((2γ/((3-2α)γ-2))<p<(2γ/((2α-1)γ+2)))有界性.

On the basis of Littlewood-Paley theory and Fourier transforms, this paper is devoted to study of a class of Marcinkiewicz integral operators associated with Surfaces of Revolution on R^n. Some rather weak size condi-tions, which imply the L^P-boundedness of these operators for some 2γ/（3-2α）γ-2〈2γ/（2α-1）γ＋2are given.