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The sharp bound for the Hilbert transform on weighted Lebesgue spaces in terms of the classical A p characteristic

From: American Journal of Mathematics
Volume 129, Number 5, October 2007
pp. 1355-1375 | 10.1353/ajm.2007.0036


We show that the norm of the Hilbert transform as an operator in the weighted space

(ω) for 2 ≤ p p characteristic of ω. This result is sharp. We also prove a bilinear imbedding theorem with simple conditions.