Cauchy transform and Poisson's equation

David Kalaj

Let $u\in W_0^{2,p}$, $1\le p\le \infty$ be a solution of the Poisson equation $\Delta u=h$, $h\in L^p$, in the unit disk. It is proved that $\Vert \nabla u{\Vert }_{L^p}\le a_p\Vert h{\Vert }_{L^p}$ wit…