Maximal operators and Hilbert transforms along variable non-flat homogeneous curves

Shaoming Guo, Jonathan Hickman, Victor Lie +1

We prove that the maximal operator associated with variable homogeneous planar curves $(t,u{t}^{\alpha }{)}_{t\in \mathbb{R}}$, $\alpha \ne 1$ positive, is bounded on $L^p({\mathbb{R}}^2)$ for each…