Maximal operators and Hilbert transforms along flat curves near L1

Richard Bez

doi:10.1017/S1446788709000111

Maximal operators and Hilbert transforms along flat curves near L1

Richard Bez

Mathematics

Research output: Contribution to journal › Article › peer-review

124 Downloads (Pure)

Abstract

For a class of convex curves in R-d we prove that the corresponding maximal operator and Hilbert transform are of weak type L log L. The point of interest here is that this class admits Curves which are infinitely flat at the origin. We also prove in analogous weak type result for a class of nonconvex hypersurfaces.

Original language	English
Pages (from-to)	311-323
Number of pages	13
Journal	Journal of the Australian Mathematical Society
Volume	87
Issue number	03
DOIs	https://doi.org/10.1017/S1446788709000111
Publication status	Published - 1 Dec 2009

Keywords

Hilbert transform
maximal operator
weak type estimate

Access to Document

10.1017/S1446788709000111

Bez2009S1446788709000111a
© Cambridge University Press 2009 Eligibility for repository: checked July 2014
Final published version, 173 KBLicence: None: All rights reserved

New Approaches to Central Problems in Euclidean Harmonic Analysis and Geometric Combinatorics
Bennett, J.
Engineering & Physical Science Research Council
3/01/07 → 2/01/10
Project: Research Councils

Cite this

@article{be41fbf90dfd4bf9abe15f22c1d5595b,

title = "Maximal operators and Hilbert transforms along flat curves near L1",

abstract = "For a class of convex curves in R-d we prove that the corresponding maximal operator and Hilbert transform are of weak type L log L. The point of interest here is that this class admits Curves which are infinitely flat at the origin. We also prove in analogous weak type result for a class of nonconvex hypersurfaces.",

keywords = "Hilbert transform, maximal operator, weak type estimate",

author = "Richard Bez",

year = "2009",

month = dec,

day = "1",

doi = "10.1017/S1446788709000111",

language = "English",

volume = "87",

pages = "311--323",

journal = "Journal of the Australian Mathematical Society",

publisher = "Cambridge University Press",

number = "03",

}

TY - JOUR

T1 - Maximal operators and Hilbert transforms along flat curves near L1

AU - Bez, Richard

PY - 2009/12/1

Y1 - 2009/12/1

N2 - For a class of convex curves in R-d we prove that the corresponding maximal operator and Hilbert transform are of weak type L log L. The point of interest here is that this class admits Curves which are infinitely flat at the origin. We also prove in analogous weak type result for a class of nonconvex hypersurfaces.

AB - For a class of convex curves in R-d we prove that the corresponding maximal operator and Hilbert transform are of weak type L log L. The point of interest here is that this class admits Curves which are infinitely flat at the origin. We also prove in analogous weak type result for a class of nonconvex hypersurfaces.

KW - Hilbert transform

KW - maximal operator

KW - weak type estimate

U2 - 10.1017/S1446788709000111

DO - 10.1017/S1446788709000111

M3 - Article

VL - 87

SP - 311

EP - 323

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 03

ER -

Maximal operators and Hilbert transforms along flat curves near L1

Abstract

Keywords

Access to Document

Fingerprint

Projects

New Approaches to Central Problems in Euclidean Harmonic Analysis and Geometric Combinatorics

Cite this