Maximal operators along flat curves with one variable vector field (Q6657215)

In this paper, the authors consider a maximal operator defined by a convex function \(\gamma[0;1)\) and a measurable function \(m\). Under the assumption of the doubling property of \(\gamma'\) and \(1\leqslant m(x_1)\leqslant 2\), they prove the \(L^p(R^2)\) boundedness of the maximal average. As a corollary, they obtain the pointwise convergence of the average in \(r>0\) without any size assumption for a measurable \(m\).