$L^p$ bound for the Hilbert transform along variable non-flat curves

Renhui Wan

We prove the $L^p$ bound for the Hilbert transform along variable non-flat curves $(t,u(x)[t{]}^{\alpha }+v(x)[t{]}^{\beta })$, where $\alpha$ and $\beta$ satisfy $\alpha \ne \beta ,\alpha \ne 1,\beta \ne 1.$ Comparing with…