Affordable Access

New estimates for the Beurling-Ahlfors operator on differential forms

Authors
  • Petermichl, Stefanie
  • Slavin, Leonid
  • Wick, Brett D.
Type
Published Article
Publication Date
Jan 03, 2009
Submission Date
Jan 03, 2009
Source
arXiv
License
Yellow
External links

Abstract

We establish new $p$-estimates for the norm of the generalized Beurling--Ahlfors transform $\mathcal{S}$ acting on form-valued functions. Namely, we prove that $\norm{\mathcal{S}}_{L^p(\R^n;\Lambda)\to L^p(\R^n;\Lambda)}\leq n(p^{*}-1)$ where $p^*=\max\{p, p/(p-1)\},$ 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.

Report this publication

Statistics

Seen <100 times