Journal of the
Korean Mathematical Society JKMS

In this paper we shall prove some weighted norm inequalities of the form $$\int_{R^n}|Tf(x)|^pu(x)dx\leq C_p\int_{R^n}|f(x)|^pNu(x)dx$$ for certain rough singular integral $T$ and maximal singular integral $T^*$. Here $u$ is a nonnegative measurable function on $R^n$ and $N$ denotes some maximal operator. As a consequence, some vector valued inequalities for both $T$ and $T^*$ are obtained. We shall also get a boundedness result of $T$ on the Triebel-Lizorkin spaces.

Keywords: singular integral, weighted norm inequality, vector valued inequality

MSC numbers: Primary 42B25