We investigate boundedness properties of two singular integral operators defined on Lp-spaces (1 < p < ∞) on the real line, both as convolution operators on Lp(R) and on the spaces Lp(w), where w(x) = 1/2cosh πx/2. It is proved that both operators are bounded on these spaces and estimates of the norms are obtained. This is achieved by first proving boundedness for p = 2 and weak boundedness for p = 1, and then using interpolation to obtain boundedness for 1 < p ≤ 2. To obtain boundedness also for 2 ≤ p < ∞, we use duality in the translation invariant case, while the weighted case is partly based on the expositions on the conjugate function operator in [7].
π/2