Abstract
AbstractThe long‐standing conjecture that for the norm of the Riesz–Titchmarsh discrete Hilbert transform is the same as the norm of the classical Hilbert transform, is verified when or , for . The proof, which is algebraic in nature, depends in a crucial way on the sharp estimate for the norm of a different variant of this operator for the full range of . The latter result was recently proved by the authors (Duke Math. J. 168 (2019), no. 3, 471–504).
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