Weak-type (1,1) bounds for oscillatory singular integrals with rational phases

Magali Folch-Gabayet, James Wright

Type: Article

Publication Date: 2012-01-01

Citations: 12

DOI: https://doi.org/10.4064/sm210-1-4

Abstract

We consider singular integral operators on ${\Bbb R}$ given by convolution with a principal value distribution defined by integrating against oscillating kernels of the form $e^{i R(x)}/x$ where $R(x) = P(x)/Q(x)$ is a general rational function with real

Locations

Studia Mathematica - View - PDF

Similar Works

Action	Title	Year	Authors
+	Weak (1, 1) Estimate for Oscillatory Singular Integrals with Real- Analytic Phases	1994	Yibiao Pan
+	Uniform Weak (1,1) Bounds for Oscillatory Singular Integrals	1995	Yibiao Pan
+	Uniform $$L^p$$ Boundedness for Oscillatory Singular Integrals with $$C^\infty $$ Phases	2022	Yibiao Pan
+	A Class of Oscillatory Singular Integrals with Rough Kernels and Fewnomials Phases	2024	Jiao Ma Chenyan Wang Huoxiong Wu
+	Weak (1,1) bounds for oscillatory singular integrals	1987	Sagun Chanillo Michael Christ
+	Weak (1,1) Boundedness of Oscillatory Singular Integral with Variable Phase	2019	Hai Xia Yu Junfeng Li
+ PDF Chat	On the weak (1,1) boundedness of a class of oscillatory singular integrals	1993	Yibiao Pan
+ PDF Chat	Weak (1,1) estimate for oscillatory singular integrals with real-analytic phases	1994	Yibiao Pan
+	Oscillatory Singular Integral Operators with Hölder Class Kernels	2019	Hussain Al-Qassem Leslie Cheng Yibiao Pan
+	Uniform boundedness of oscillatory singular integrals with rational phases	2025	Hussain Al-Qassem Leslie Cheng Yibiao Pan
+	Sharp bounds for oscillatory singular integrals on Hardy spaces	2017	Hussain Al-Qassem Leslie Cheng Yibiao Pan
+	Uniform Estimates for Oscillatory Integral Operators with Polynomial Phases	2024	Zuoshunhua Shi
+ PDF Chat	Sharp $$L^{p}$$ L p -boundedness of oscillatory integral operators with polynomial phases	2016	Zuoshunhua Shi Dunyan Yan
+ PDF Chat	Rational Approximation, Oscillatory Cauchy Integrals, and Fourier Transforms	2015	Thomas Trogdon
+ PDF Chat	Sharp $L^2$ bounds for oscillatory integral operators with $C^\infty$ phases	2001	Slava Rychkov
+	Approximating periodic functions in Hölder type metrics by singular integrals with positive Kernels	2008	Anna S. Zhuk
+	Decay estimates for oscillatory integrals with polynomial phase	2003	Brian Felkel
+ PDF Chat	A note on singular oscillatory integrals with certain rational phases	2023	Chenyan Wang Huoxiong Wu
+	Sharp Estimates of Oscillatory Singular Integrals with Rough Kernels	2015	Hussain Al-Qassem Leslie Cheng Yubin Pan
+ PDF Chat	SHARP Lp DECAY ESTIMATES FOR DEGENERATE AND SINGULAR OSCILLATORY INTEGRAL OPERATORS: HOMOGENEOUS POLYNOMIAL PHASES	2024	Shaozhen Xu

Works That Cite This (12)

Action	Title	Year	Authors
+	A Weak Type Inequality for Maximal Monomial Oscillatory Hilbert Transforms	2016	Ben Krause Michael T. Lacey
+	Weak (1,1) Boundedness of Oscillatory Singular Integral with Variable Phase	2019	Hai Xia Yu Junfeng Li
+	Oscillatory Singular Integral Operators with Hölder Class Kernels	2019	Hussain Al-Qassem Leslie Cheng Yibiao Pan
+ PDF Chat	Weak-Type (1, 1) Estimates for Strongly Singular Operators	2019	Magali Folch-Gabayet Roberto A. Saenz
+ PDF Chat	Oscillatory integrals related to Carleson's theorem: fractional monomials	2016	Shaoming Guo
+ PDF Chat	Logarithmic Bounds for Oscillatory Singular Integrals on Hardy Spaces	2016	Hussain Al-Qassem Leslie Cheng Yibiao Pan
+	Endpoint Estimates for Oscillatory Singular Integrals with Hölder Class Kernels	2019	Hussain Al-Qassem Leslie Cheng Yibiao Pan
+	Weak-type (1,1) estimates for strongly singular operators	2018	Magali Folch-Gabayet Ricardo A. Sáenz
+	Weak Type Bound for Oscillatory Singular Integrals	2016	Michael T. Lacey
+	Sparse Bounds for Oscillatory and Random Singular Integrals	2016	Michael T. Lacey Scott Spencer

Works Cited by This (10)

Action	Title	Year	Authors
+ PDF Chat	Hilbert integrals, singular integrals, and Radon transforms I	1986	D. H. Phong E. M. Stein
+	Weak (1,1) bounds for oscillatory singular integrals	1987	Sagun Chanillo Michael Christ
+ PDF Chat	Singular integral operators associated to curves with rational components	2007	Magali Folch-Gabayet James Wright
+ PDF Chat	Hardy Spaces and Oscillatory Singular Integrals	1991	Yibiao Pan
+ PDF Chat	Inequalities for strongly singular convolution operators	1970	Charles Fefferman
+ PDF Chat	An oscillatory integral estimate associated to rational phases	2003	Magali Folch-Gabayet James Wright
+	Harmonic analysis on nilpotent groups and singular integrals I. Oscillatory integrals	1987	Fulvio Ricci E. M. Stein
+ PDF Chat	Hp spaces of several variables	1972	Charles Fefferman E. M. Stein
+ PDF Chat	Maximal functions and Hilbert transforms associated to polynomials	1998	Anthony Carbery Fulvio Ricci James Wright
+ PDF Chat	Boundedness of certain oscillatory singular integrals	1995	Dashan Fan Yibiao Pan