SU\G(𝔸)/K·U

<i>L</i><sup><i>p</i></sup>estimates for operators associated to flat curves without the Fourier transform

Anthony Carbery, James Vance, Stephen Wainger, David Watson, James Wright

Type: Article

Publication Date: 1995-02-01

Citations: 6

DOI: https://doi.org/10.2140/pjm.1995.167.243

Abstract

The purpose of this paper is to provide new proofs to known theorems on the L p boundedness of the maximal function and Hubert transform corresponding to curves in R n which are "infinitely flat" at the origin.The old proofs use the Fourier transform in a crucial way.The present proofs avoid the Fourier transform and hence at least have the potential of being used in more general situations.

Locations

  • Pacific Journal of Mathematics - View - PDF

Similar Works

Action Title Year Authors
+ PDF Chat <i>L</i><sup><i>p</i></sup>-boundedness of the Hilbert transform and maximal function along flat curves in ℝ<sup><i>n</i></sup> 1995 Sarah Ziesler
+ L p -Boundedness of the Hilbert Transform and Maximal Function Associated to Flat Plane Curves 1994 S. Ziesler
+ The function spaces <i>L<sup>p</sup></i>, 1 ≤ <i>p</i> ≤ ∞ 2005 René L. Schilling
+ Fourier theorems for functions outside <i>L<sup>p</sup></i> 1987 D. C. Champeney
+ PDF Chat $$L^2$$ boundedness of Hilbert transforms along variable flat curves 2021 Junfeng Li
Haixia Yu
+ PDF Chat 𝐿^{𝑝} estimates for maximal functions and Hilbert transforms along flat convex curves in 𝐑² 1986 Hasse Carlsson
Michael Christ
Antonio Córdoba
Javier Duoandikoetxea
José L. Rubio de Francia
James Vance
Stephen Wainger
David A. Weinberg
+ PDF Chat MAXIMAL OPERATORS AND HILBERT TRANSFORMS ALONG FLAT CURVES NEAR <i>L</i><sup>1</sup> 2009 Neal Bez
+ Sharp L 2 boundedness of the oscillatory hyper-Hilbert transform along curves 2010 Jie Cheng Chen
Da Shan Fan
Xiang Zhu
+ $L^p$ estimates for Hilbert transform and maximal operator associated to variable polynomial 2022 Renhui Wan
+ PDF Chat A maximal restriction theorem and Lebesgue points of functions in $\mathcal F(L^p)$ 2019 Detlef Müller
Fulvio Ricci
James Wright
+ PDF Chat Hilbert transforms and maximal functions along variable flat curves 2002 Jonathan Bennett
+ PDF Chat Maximal functions and Hilbert Transforms along variable flat curves 1999 Anthony Carbery
Sonsoles Pérez
+ The Fourier Transform in <i>L</i><sup><i>p</i></sup>-Spaces 2018
+ Harnack Extension and Convergence Theorems for the <i>H</i>-Integral 2017
+ Lp$L^p$ bound for the Hilbert transform along variable non‐flat curves 2023 Renhui Wan
+ PDF Chat 𝐿^{𝑝}-boundedness of the Hilbert transform and maximal function associated to flat plane curves 1994 Sarah Ziesler
+ A maximal restriction theorem and Lebesgue points of functions in F(L^p) 2016 Detlef Müller
Fulvio Ricci
James Wright
+ PDF Chat <i>L</i><sup><i>p</i></sup>estimates for the Hilbert transforms along a one-variable vector field 2013 Michael Bateman
Christoph Thiele
+ On Criteria for Fourier Constants of <i>L</i> Integrable Functions 1933 Charles N. Moore
+ On Certain Criteria for Fourier Constants of <i>L</i> Integrable Functions 1932 Charles N. Moore

Works That Cite This (5)

Action Title Year Authors
+ PDF Chat The Calderón commutator along a parabola 1999 Anthony Carbery
Steve Hofmann
James Wright
+ PDF Chat Fourier restriction to polynomial curves I: a geometric inequality 2010 Spyridon Dendrinos
James Wright
+ PDF Chat Hilbert transforms and maximal functions associated to flat curves on the Heisenberg group 1995 Anthony Carbery
Stephen Wainger
James Wright
+ The Calder\'{o}n Commutator Along a Parabola 1997 Anthony Carbery
Steve Hofmann
James Wright
+ The Hilbert transform along the extended evil ladder curve 1999 Wu Baoyi
Weiyi Su

Works Cited by This (8)

Action Title Year Authors
+ Singular Integrals and Differentiability Properties of Functions. 1971 Elias M. Stein
+ Harmonic analysis on nilpotent groups and singular integrals. II. Singular kernels supported on submanifolds 1988 Fulvio Ricci
Elias M. Stein
+ Operators associated to flat plane curves: Lp estimates via dilation methods 1989 Anthony Carbery
Michael Christ
James Vance
Stephen Wainger
David K. Watson
+ PDF Chat Differentiation in lacunary directions 1978 Alexander Nagel
E. M. Stein
Stephen Wainger
+ PDF Chat Inequalities for strongly singular convolution operators 1970 Charles Fefferman
+ The Hilbert Transform for Convex Curves in R n 1986 Alexander Nagel
James Vance
Stephen Wainger
David A. Weinberg
+ Hilbert Transforms Along Curves: I. Nilpotent Groups 1985 Michael Christ
+ Hilbert transforms and maximal functions related to variable curves 1979 Alexander Nagel
Elias M. Stein
Stephen Wainger