Marcinkiewicz integral on weighted Hardy spaces

Yong Ding; Ming Yi Lee; Chin Cheng Lin

doi:10.1007/s00013-003-4660-x

Marcinkiewicz integral on weighted Hardy spaces

Yong Ding, Ming Yi Lee, Chin Cheng Lin

Department of Mathematics

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

11 Scopus citations

Abstract

In this paper we give sufficient conditions to imply the H_w ¹-L_w¹ boundedness, of the Marcinkiewicz integral operator μ_ω, where w is a Muckenhoupt weight. We also prove that, under the stronger condition ω ∈ Lip _α, the operator μ_ω is bounded from H _w^p to L_w^p for max{n/(n + 1/2), n/(n + α)} < p < 1.

Original language	English
Pages (from-to)	620-629
Number of pages	10
Journal	Archiv der Mathematik
Volume	80
Issue number	6
DOIs	https://doi.org/10.1007/s00013-003-4660-x
State	Published - 1 Jun 2003

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abstract = "In this paper we give sufficient conditions to imply the Hw 1-Lw1 boundedness, of the Marcinkiewicz integral operator μω, where w is a Muckenhoupt weight. We also prove that, under the stronger condition ω ∈ Lip α, the operator μω is bounded from H wp to Lwp for max{n/(n + 1/2), n/(n + α)} < p < 1.",

author = "Yong Ding and Lee, {Ming Yi} and Lin, {Chin Cheng}",

note = "Funding Information: Research by the first author was supported by NNSF of China under Grant #10271016. Research by the third author was supported by NSC in Taipei under Grant #NSC 90-2115-M-008-018.",

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T1 - Marcinkiewicz integral on weighted Hardy spaces

AU - Ding, Yong

AU - Lee, Ming Yi

AU - Lin, Chin Cheng

N1 - Funding Information: Research by the first author was supported by NNSF of China under Grant #10271016. Research by the third author was supported by NSC in Taipei under Grant #NSC 90-2115-M-008-018.

PY - 2003/6/1

Y1 - 2003/6/1

N2 - In this paper we give sufficient conditions to imply the Hw 1-Lw1 boundedness, of the Marcinkiewicz integral operator μω, where w is a Muckenhoupt weight. We also prove that, under the stronger condition ω ∈ Lip α, the operator μω is bounded from H wp to Lwp for max{n/(n + 1/2), n/(n + α)} < p < 1.

AB - In this paper we give sufficient conditions to imply the Hw 1-Lw1 boundedness, of the Marcinkiewicz integral operator μω, where w is a Muckenhoupt weight. We also prove that, under the stronger condition ω ∈ Lip α, the operator μω is bounded from H wp to Lwp for max{n/(n + 1/2), n/(n + α)} < p < 1.

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DO - 10.1007/s00013-003-4660-x

M3 - 期刊論文

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SN - 0003-889X

VL - 80

SP - 620

EP - 629

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 6

ER -

Marcinkiewicz integral on weighted Hardy spaces

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