On weighted norm inequalities for the Carleson and Walsh–Carleson operator

摘要: We prove L(w) bounds for the Carleson operator C, its lacunary version Clac, and analogue Walsh series W in terms of Aq constants [w]Aq 1 q p. In particular, we show that, exactly as Hilbert transform, ‖C‖Lp(w) is bounded linearly by < also obtain [w]Ap , whose sharpness related to certain conjectures (for instance, Konyagin [International Congress Mathematicians, vol. II (European Mathematical Society, Zurich, 2006) 1393–1403]) on pointwise convergence Fourier functions near L. Our approach works general context maximally modulated Calderon–Zygmund operators.