$L^2$ boundedness for maximal commutators with rough variable kernels
$L^2$ boundedness for maximal commutators with rough variable kernels
For b\in BMO(\mathbb{R}^n) and k\in\mathbb{N} , the k -th order maximal commutator of the singular integral operator T with rough variable kernels is defined by T^{\ast}_{b,k}f(x) = \sup_{\varepsilon > 0} \biggl| \int_{|x-y| > \varepsilon} \frac{\Omega(x,x-y)}{|x-y|^n} (b(x)-b(y))^{k} f(y) dy \biggl|. In this paper the authors prove that the k -th order …