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A Note on the Polynomial Carleson Operator in higher dimensions
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abstract
We prove the $L^p$-boundedness, $1<p<\infty$, of the Polynomial Carleson operator in general dimension. This follows the author's resolution of the one dimensional case as well as the work of Zorin-Kranich on the higher dimensional case in the setting $2\leq p<\infty$. The techniques used in this paper are direct adaptations and natural extensions to the higher dimensional case of the one-dimensional methods developed by the author.
Forward citations
Cited by 2 Pith papers
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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.
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The Bilinear Hilbert-Carleson operator along curves. The purely non-zero curvature case
The Bilinear Hilbert-Carleson operator along the moment curve (t, t^2, t^3) satisfies the expected L^{p1} x L^{p2} to L^r bounds for 1 < p1, p2 < infinity and 1/2 < r < infinity.
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