Bi-parameter Littlewood–Paley operators with upper doubling measures

Mingming Cao; Qingying Xue

doi:10.1215/ijm/1520046209

Bi-parameter Littlewood–Paley operators with upper doubling measures

Mingming Cao
, Qingying Xue^*

^*Corresponding author for this work

Beijing Normal University

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

1 Scopus citations

Abstract

Let μ = μ_n1 ×μ_n2, where μ_n1 and μ_n2 are upper doubling measures on ℝⁿ¹ and ℝⁿ², respectively. Let the pseudo-accretive function b = b₁ ⊗ b₂ satisfy a bi-parameter Carleson condition. In this paper, we established the L² (μ) boundedness of non-homogeneous Littlewood–Paley g*_λ-function^∗ with non-convolution type kernels on product spaces. This was mainly done by means of dyadic analysis and non-homogenous methods. The result is new even in the setting of Lebesgue measures.

Original language	English
Pages (from-to)	53-79
Number of pages	27
Journal	Illinois Journal of Mathematics
Volume	61
Issue number	1-2
DOIs	https://doi.org/10.1215/ijm/1520046209
State	Published - 2017
Externally published	Yes

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title = "Bi-parameter Littlewood–Paley operators with upper doubling measures",

abstract = "Let μ = μn1 ×μn2, where μn1 and μn2 are upper doubling measures on ℝn1 and ℝn2, respectively. Let the pseudo-accretive function b = b1 ⊗ b2 satisfy a bi-parameter Carleson condition. In this paper, we established the L2 (μ) boundedness of non-homogeneous Littlewood–Paley g*λ-function∗ with non-convolution type kernels on product spaces. This was mainly done by means of dyadic analysis and non-homogenous methods. The result is new even in the setting of Lebesgue measures.",

author = "Mingming Cao and Qingying Xue",

note = "Publisher Copyright: {\textcopyright} 2018 University of Illinois.",

year = "2017",

doi = "10.1215/ijm/1520046209",

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T1 - Bi-parameter Littlewood–Paley operators with upper doubling measures

AU - Cao, Mingming

AU - Xue, Qingying

PY - 2017

Y1 - 2017

N2 - Let μ = μn1 ×μn2, where μn1 and μn2 are upper doubling measures on ℝn1 and ℝn2, respectively. Let the pseudo-accretive function b = b1 ⊗ b2 satisfy a bi-parameter Carleson condition. In this paper, we established the L2 (μ) boundedness of non-homogeneous Littlewood–Paley g*λ-function∗ with non-convolution type kernels on product spaces. This was mainly done by means of dyadic analysis and non-homogenous methods. The result is new even in the setting of Lebesgue measures.

AB - Let μ = μn1 ×μn2, where μn1 and μn2 are upper doubling measures on ℝn1 and ℝn2, respectively. Let the pseudo-accretive function b = b1 ⊗ b2 satisfy a bi-parameter Carleson condition. In this paper, we established the L2 (μ) boundedness of non-homogeneous Littlewood–Paley g*λ-function∗ with non-convolution type kernels on product spaces. This was mainly done by means of dyadic analysis and non-homogenous methods. The result is new even in the setting of Lebesgue measures.

UR - https://www.scopus.com/pages/publications/85042771093

U2 - 10.1215/ijm/1520046209

DO - 10.1215/ijm/1520046209

M3 - 文章

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VL - 61

SP - 53

EP - 79

JO - Illinois Journal of Mathematics

JF - Illinois Journal of Mathematics

IS - 1-2

ER -

Bi-parameter Littlewood–Paley operators with upper doubling measures

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