Sharp $L^p$ estimates of powers of the complex Riesz transform

Andrea Carbonaro, Oliver Dragičević, Vjekoslav Kovač

Let $R_{1,2}$ be scalar Riesz transforms on ${\mathbb{R}}^2$. We prove that the $L^p$ norms of $k$-th powers of the operator $R_2+i{R}_1$ behave exactly as $|k{|}^{1-2/p}p$, uniformly in…