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The sharp $L^p$ bound for the imaginary part of the Beurling-Ahlfors operator on the lattice
We prove the sharp $\ell^p$ bound $p^\star-1$ for certain second-order discrete Riesz transforms on products of integers, in all dimensions. The family includes the imaginary part of the discrete Beurling-Ahlfors operator in dimension two as a special case. While these operators admit a martingale r
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