Feng Liu

Weighted Endpoint Variational and Jump Inequalites for Rough Singular Integrals

In this present paper, we study the weighted weak type $(1,\,1)$ bounds for rough maximal singular integral operators as well as the the corresponding variation and jump operators. Our first result is the weighted weak type $(1,\,1)$ bound for the maximal singular integral $$T_{\Omega}^{*}f(x)=\sup\limits_{\varepsilon>...