Hostname: page-component-cb9f654ff-mx8w7 Total loading time: 0 Render date: 2025-08-20T11:53:35.655Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimates for maximal singular integral operators in non-homogeneous spaces

Published online by Cambridge University Press:  12 July 2007

Guoen Hu ,
Yan Meng  and
Dachun Yang
Guoen Hu
Affiliation:
Department of Applied Mathematics, University of Information Engineering, PO Box 1001-747, Zhengzhou 450002, People's Republic of China (huguoen@eyou.com)
Yan Meng
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People's Republic of Chinamengyan@mail.bnu.edu.cn
Dachun Yang
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People's Republic of Chinadcyang@bnu.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

Under the assumption that the Radon measure μ on Rd satisfies only some growth condition, the authors prove that, for the maximal singular integral operator associated with a singular integral whose kernel only satisfies a standard size condition and the Hörmander condition, its boundedness in Lebesgue spaces Lp(μ) for any p ∈ (1, ∞) is equivalent to its boundedness from L1(μ) into weak L1(μ). As an application, the authors verify that if the truncated singular integral operators are bounded on L2(μ) uniformly, then the associated maximal singular integral operator is also bounded on Lp(μ) for any p ∈ (1, ∞).

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 2 , April 2006 , pp. 351 - 364
Copyright
Copyright © Royal Society of Edinburgh 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable