New estimates for the Beurling-Ahlfors operator on differential forms
arXiv:0901.0345
Abstract
We establish new -estimates for the norm of the generalized Beurling--Ahlfors transform acting on form-valued functions. Namely, we prove that $\norm{\mathcal{S}}_{L^p(\R^n;Λ)\to L^p(\R^n;Λ)}\leq n(p^{*}-1)$ where thus extending the recent Nazarov--Volberg estimates to higher dimensions. The even-dimensional case has important implications for quasiconformal mappings. Some promising prospects for further improvement are discussed at the end.
v1: 17 pages