On the norm of the Beurling-Ahlfors operator in several dimensions
classification
🧮 math.CA
math.PR
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beurling-ahlforsdimensionsnormoperatorbottomburkholderearlierextension
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The Lp operator norm of the generalized Beurling-Ahlfors transformation in n variables is at most (n/2+1)(p-1) for p>2. This improves on earlier results in all dimensions n>2. 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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