Uniform Bounds for Oscillatory and Polynomial Carleson Operators

被引：0
作者：
João P. G. Ramos
机构：
[1] ETH Zürich,
[2] D-Math,undefined
来源：
Journal of Fourier Analysis and Applications | 2021年 / 27卷
关键词：
Carleson operators; Time-frequency analysis; Singular integrals; Oscillatory integrals; Uniform estimates; 42A20; 42A50; 42B25;
D O I：
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学科分类号：
摘要：
We prove that a variety of oscillatory and polynomial Carleson operators are uniformly bounded on the family of parameters under considerations. As a particular application of our techniques, we prove uniform bounds for oscillatory Carleson operators near a single scale version of the quadratic Carleson operator.
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[1]  
Carbery A(1998)Maximal functions and Hilbert transforms associated to polynomials Rev. Mat. Iberoam. 14 117-144
[2]  
Ricci F(1966)On convergence and growth of partial sums of Fourier series Acta Math. 116 135-157
[3]  
Wright J(1985)Hilbert transforms along curves: I. Nilpotent groups Ann. Math. 122 575-596
[4]  
Carleson L(1987)A remark on singular Calderón–Zygmund theory Proc. Am. Math. Soc. 99 71-75
[5]  
Christ M(1966)Singular integrals with mixed homogeneity Stud. Math. 27 19-38
[6]  
Christ M(1973)Pointwise convergence of Fourier series Ann. Math. 98 551-571
[7]  
Stein E(2017)A remark on oscillatory integrals associated with fewnomials N. Y. J. Math. 23 1733-1738
[8]  
Fabes E(2016)Oscillatory integrals related to Carleson’s theorem: fractional monomials Commun. Pure Appl. Anal. 15 929-946
[9]  
Riviére N(2017)Polynomial Carleson operators along monomial curves in the plane J. Geom. Anal. 27 2977-3012
[10]  
Fefferman C(2017)Maximal operators and Hilbert transforms along variable non-flat homogeneous curves Proc. Lond. Math. Soc. 115 177-219
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