Maximal functions and singular integrals associated to polynomial mappings of IRn

A  Carbery; Fulvio Ricci; J  Wright

Maximal functions and singular integrals associated to polynomial mappings of IRn

A Carbery, Fulvio Ricci, J Wright

School of Mathematics

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

Abstract

We consider convolution operators on R-n of the form

T(P)f(x) = integral(Rm) f(x - P(y))K(y)dy,

where P is a polynomial defined on R-m with values in R-n and K is a smooth Calderon-Zygmund kernel on R-m. A maximal operator M-P can be constructed in a similar fashion. We discuss weak-type 1-1 estimates for T-P and M-P and the uniformity of such estimates with respect to P. We also obtain L-p-estimates for "supermaximar' operators, defined by taking suprema over P ranging in certain classes of polynomials of bounded degree.

Original language	English
Pages (from-to)	122
Number of pages	22
Journal	Revista Matemática Iberoamericana
Volume	19
Issue number	1
Publication status	Published - 2003

Keywords / Materials (for Non-textual outputs)

maximal functions
singular integrals
weak-type estimates
HILBERT-TRANSFORMS
HARMONIC-ANALYSIS
NILPOTENT GROUPS
ROUGH OPERATORS
KERNELS
BOUNDS

Cite this

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title = "Maximal functions and singular integrals associated to polynomial mappings of IRn",

abstract = "We consider convolution operators on R-n of the formT(P)f(x) = integral(Rm) f(x - P(y))K(y)dy,where P is a polynomial defined on R-m with values in R-n and K is a smooth Calderon-Zygmund kernel on R-m. A maximal operator M-P can be constructed in a similar fashion. We discuss weak-type 1-1 estimates for T-P and M-P and the uniformity of such estimates with respect to P. We also obtain L-p-estimates for {"}supermaximar' operators, defined by taking suprema over P ranging in certain classes of polynomials of bounded degree.",

keywords = "maximal functions, singular integrals, weak-type estimates, HILBERT-TRANSFORMS, HARMONIC-ANALYSIS, NILPOTENT GROUPS, ROUGH OPERATORS, KERNELS, BOUNDS",

author = "A Carbery and Fulvio Ricci and J Wright",

year = "2003",

language = "English",

volume = "19",

pages = "122",

journal = "Revista Matem{\'a}tica Iberoamericana",

issn = "0213-2230",

publisher = "Universidad Autonoma de Madrid",

number = "1",

}

TY - JOUR

T1 - Maximal functions and singular integrals associated to polynomial mappings of IRn

AU - Carbery, A

AU - Ricci, Fulvio

AU - Wright, J

PY - 2003

Y1 - 2003

N2 - We consider convolution operators on R-n of the formT(P)f(x) = integral(Rm) f(x - P(y))K(y)dy,where P is a polynomial defined on R-m with values in R-n and K is a smooth Calderon-Zygmund kernel on R-m. A maximal operator M-P can be constructed in a similar fashion. We discuss weak-type 1-1 estimates for T-P and M-P and the uniformity of such estimates with respect to P. We also obtain L-p-estimates for "supermaximar' operators, defined by taking suprema over P ranging in certain classes of polynomials of bounded degree.

AB - We consider convolution operators on R-n of the formT(P)f(x) = integral(Rm) f(x - P(y))K(y)dy,where P is a polynomial defined on R-m with values in R-n and K is a smooth Calderon-Zygmund kernel on R-m. A maximal operator M-P can be constructed in a similar fashion. We discuss weak-type 1-1 estimates for T-P and M-P and the uniformity of such estimates with respect to P. We also obtain L-p-estimates for "supermaximar' operators, defined by taking suprema over P ranging in certain classes of polynomials of bounded degree.

KW - maximal functions

KW - singular integrals

KW - weak-type estimates

KW - HILBERT-TRANSFORMS

KW - HARMONIC-ANALYSIS

KW - NILPOTENT GROUPS

KW - ROUGH OPERATORS

KW - KERNELS

KW - BOUNDS

M3 - Article

SN - 0213-2230

VL - 19

SP - 122

JO - Revista Matemática Iberoamericana

JF - Revista Matemática Iberoamericana

IS - 1

ER -

Maximal functions and singular integrals associated to polynomial mappings of IRn

Abstract

Keywords / Materials (for Non-textual outputs)

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