The maximal degree-one resonant Carleson-Radon transform CR^*_V is L^p-bounded for 1<p<∞ in all dimensions D≥1 when V admits a nontrivial perpendicular vector in the first D coordinates.
& Thiele, C.L p estimates for the Hilbert transforms along a one-variable vector field.Anal
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On the resonant Carleson-Radon transform in all dimensions. The degree one resonant case
The maximal degree-one resonant Carleson-Radon transform CR^*_V is L^p-bounded for 1<p<∞ in all dimensions D≥1 when V admits a nontrivial perpendicular vector in the first D coordinates.