On Polynomial Carleson Operators Along Quadratic Hypersurfaces
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Author(s)
Anderson, Theresa C.
Maldague, Dominique
Pierce, Lillian B.
Yung, Po-Lam
Date Issued
August 23, 2024
Journal
The Journal of Geometric Analysis
Publisher
Springer US
Citation
Anderson, T.C., Maldague, D., Pierce, L.B. et al. On Polynomial Carleson Operators Along Quadratic Hypersurfaces. J Geom Anal 34, 321 (2024).
Version
Author's final manuscript
Abstract
We prove that a maximally modulated singular oscillatory integral operator along a hypersurface defined by ( y , Q ( y ) ) ⊆ R n + 1 , for an arbitrary non-degenerate quadratic form Q, admits an a priori bound on L p for all 1 < p < ∞ , for each n ≥ 2 . This operator takes the form of a polynomial Carleson operator of Radon-type, in which the maximally modulated phases lie in the real span of { p 2 , … , p d } for any set of fixed real-valued polynomials p j such that p j is homogeneous of degree j, and p 2 is not a multiple of Q(y). The general method developed in this work applies to quadratic forms of arbitrary signature, while previous work considered only the special positive definite case Q ( y ) = | y | 2 .
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s12220-024-01676-9
