$L^p$–bounds for the Beurling–Ahlfors transform
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- by Rodrigo Bañuelos and Prabhu Janakiraman PDF
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Abstract:
Let $B$ denote the Beurling–Ahlfors transform defined on $L^p(\mathbb {C})$, $1<p<\infty$. The celebrated conjecture of T. Iwaniec states that its $L^p$ norm $\|B\|_p=p^*-1$ where $p^*= \max \{p,\frac {p}{p-1}\}$. In this paper the new upper estimate \[ \|B\|_p\leq 1.575 (p^*-1), \hspace {3mm} 1<p<\infty ,\] is found.References
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Additional Information
- Rodrigo Bañuelos
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395
- MR Author ID: 30705
- Email: banuelos@math.purdue.edu
- Prabhu Janakiraman
- Affiliation: Department of Mathematics, University of Illinois, Urbana-Champaign, Illinois 61801
- Email: pjanakir@math.uiuc.edu
- Received by editor(s): November 15, 2005
- Received by editor(s) in revised form: April 26, 2006
- Published electronically: February 13, 2008
- Additional Notes: The first author was supported in part by NSF grant #0603701-DMS
The second author was supported in part by an NSF VIGRE postdoctoral fellowship - © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 3603-3612
- MSC (2000): Primary 42B20, 60H05
- DOI: https://doi.org/10.1090/S0002-9947-08-04537-6
- MathSciNet review: 2386238