Mathematical Research Letters

Volume 4, Issue 4, July 1997 pp. 469-471.

Best bounds for the Hilbert transform on $L^p(\Bbb R^1)$

Authors: Loukas Grafakos
Author institution: University of Missouri

Summary: We present a short proof of the boundedness of the Hilbert transform on $L^p(\Bbb R^1)$ with the best possible constant. The proof assumes two lemmas known in the literature, but it avoids using the conjugate function on the circle and it is given directly on the line.

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