Sparse pointwise bounds for maximal truncations of rough singular integrals and Sobolev-type inequalities

Diego Chamorro, Anca-Nicoleta Marcoci, Liviu-Gabriel Marcoci

Let $1<\rho <n$ and let Omega be in $L^{\rho }(S^{(n-1)})$ with vanishing mean. We prove that the maximal truncation $T_{\Omega }^{\ast }$ of the rough singular integral $T_{\Omega }$ is pointwise dominated by…