On the Norm of the Beurling – Ahlfors Operator in Several Dimensions

@inproceedings{Hytnen2008OnTN,
  title={On the Norm of the Beurling – Ahlfors Operator in Several Dimensions},
  author={Tuomas Hyt{\"o}nen},
  year={2008}
}
The generalized Beurling–Ahlfors operator S on L(R; Λ), where Λ := Λ(R) is the exterior algebra with its natural Hilbert space norm, satisfies the estimate ‖S‖L (Lp(Rn;Λ)) ≤ (n/2 + 1)(p ∗ − 1), p∗ := max{p, p′}. This improves on earlier results in all dimensions n ≥ 3. The proof is based on the heat extension and relies at the bottom on Burkholder’s sharp inequality for martingale transforms. 

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