$L^p$--bounds for the Beurling--Ahlfors transform

By Rodrigo Bañuelos, Prabhu Janakiraman. 2008

94 citations recorded by the source corpus.

Let B denote the Beurling-Ahlfors transform defined on L p (C), 1 < p < 00. The celebrated conjecture of T. Iwaniec states that its L p norm ∥B∥ p = p* -1 1 where p* = max{p, p/p-1-}. In this paper the new upper estimate ∥B∥ p < 1.575 (p* - 1), 1 < p < ∞, is found.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/a7ba0d0d36eec9fce60a3eb6a8af854b34b9940b

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In Applied Mathematics

1. Rodrigo Bañuelos
2. Bartłlomiej Dyda
3. Mateusz Kwaśnicki
4. Krzysztof Bogdan
5. Nicolai V. Krylov

Citations in the corpus

• The foundational inequalities of D.L. Burkholder and some of their ramifications (2010, background): “ constants in Theorem 2.1.2. Motivated by the structure of the IR2-valued martingales that arise in the martingale representation for the Beurling-Ahlfors operator, the following theorem is proved in [17]. Theorem 2.2.4. Let X t= (X1,X2,...,Xm) and Yt = (Y1,Y2,...,Ym) be two IRm-valued martingales o”