$L^p$-boundedness of a singular integral operator

Canadian mathematical bulletin

关键词: singular integral;    rough kernel;    Hardy space;   

DOI  :  10.4153/CMB-1998-054-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $b(t)$ be an $L^infty$ function on $R$, $Omega (,y')$ bean $H^1$ function on the unit sphere satisfying the mean zeroproperty (1) and $Q_m(t)$ be a real polynomial on $R$ of degree$m$ satisfying $Q_m(0)=0$. We prove that the singular integraloperator $$T_{Q_m,b} (,f) (x)=p.v. int_R^n b(|y|) Omega(,y) |y|^{-n} fleft( x-Q_m (|y|) y' ight) ,dy$$is bounded in $L^p (R^n)$ for $1

【 授权许可】

Unknown