Weak Type (1,1) Behavior for the Maximal Operator with L 1-Dini Kernel

Yong Ding; Xudong Lai

doi:10.1007/s11118-017-9612-3

Weak Type (1,1) Behavior for the Maximal Operator with L ¹-Dini Kernel

Yong Ding
, Xudong Lai^*

^*Corresponding author for this work

Beijing Normal University

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

15 Scopus citations

Abstract

Let M_Ω be the maximal operator with homogeneous kernel Ω. In the present paper, we show that if Ω satisfies the L¹-Dini condition on Sⁿ⁻¹, then the following weak type (1,1) behaviors (Formula presented.) hold for the maximal operator M_Ω and f∈ L¹(ℝⁿ) , here ω~ ₁ denotes the L¹ integral modulus of continuity of Ω defined by translation in ℝⁿ.

Original language	English
Pages (from-to)	169-187
Number of pages	19
Journal	Potential Analysis
Volume	47
Issue number	2
DOIs	https://doi.org/10.1007/s11118-017-9612-3
State	Published - 1 Aug 2017
Externally published	Yes

Keywords

Homogeneous kernel
Limiting behavior
Maximal operator
Weak type

Access to Document

10.1007/s11118-017-9612-3

Cite this

@article{5ee6c0ded34845688686c3a4c0cf2579,

title = "Weak Type (1,1) Behavior for the Maximal Operator with L 1-Dini Kernel",

abstract = "Let MΩ be the maximal operator with homogeneous kernel Ω. In the present paper, we show that if Ω satisfies the L1-Dini condition on Sn−1, then the following weak type (1,1) behaviors (Formula presented.) hold for the maximal operator MΩ and f∈ L1(ℝn) , here ω\textasciitilde{} 1 denotes the L1 integral modulus of continuity of Ω defined by translation in ℝn.",

keywords = "Homogeneous kernel, Limiting behavior, Maximal operator, Weak type",

author = "Yong Ding and Xudong Lai",

note = "Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media Dordrecht.",

year = "2017",

month = aug,

day = "1",

doi = "10.1007/s11118-017-9612-3",

language = "英语",

volume = "47",

pages = "169--187",

journal = "Potential Analysis",

issn = "0926-2601",

publisher = "Springer Netherlands",

number = "2",

}

TY - JOUR

T1 - Weak Type (1,1) Behavior for the Maximal Operator with L 1-Dini Kernel

AU - Ding, Yong

AU - Lai, Xudong

PY - 2017/8/1

Y1 - 2017/8/1

N2 - Let MΩ be the maximal operator with homogeneous kernel Ω. In the present paper, we show that if Ω satisfies the L1-Dini condition on Sn−1, then the following weak type (1,1) behaviors (Formula presented.) hold for the maximal operator MΩ and f∈ L1(ℝn) , here ω~ 1 denotes the L1 integral modulus of continuity of Ω defined by translation in ℝn.

AB - Let MΩ be the maximal operator with homogeneous kernel Ω. In the present paper, we show that if Ω satisfies the L1-Dini condition on Sn−1, then the following weak type (1,1) behaviors (Formula presented.) hold for the maximal operator MΩ and f∈ L1(ℝn) , here ω~ 1 denotes the L1 integral modulus of continuity of Ω defined by translation in ℝn.

KW - Homogeneous kernel

KW - Limiting behavior

KW - Maximal operator

KW - Weak type

UR - https://www.scopus.com/pages/publications/85009348218

U2 - 10.1007/s11118-017-9612-3

DO - 10.1007/s11118-017-9612-3

M3 - 文章

AN - SCOPUS:85009348218

SN - 0926-2601

VL - 47

SP - 169

EP - 187

JO - Potential Analysis

JF - Potential Analysis

IS - 2

ER -

Weak Type (1,1) Behavior for the Maximal Operator with L ¹-Dini Kernel

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this