Mathematical Research Letters
Volume 4 (1997)
Best bounds for the Hilbert transform on $L^p(\Bbb R^1)$
Pages: 469 – 471
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.