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Article overview
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New estimates for the Beurling-Ahlfors operator on differential forms | | Stefanie Petermichl
; Leonid Slavin
; Brett D. Wick
; | | Date: |
4 Jan 2009 | | 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 $
orm{mathcal{S}}_{L^p(R^n;Lambda) o
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. | | Source: | arXiv, 0901.0345 | | Services: | Forum | Review | PDF | Favorites | |
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