A note on the limiting weak-type behavior for maximal operators
HTML articles powered by AMS MathViewer
- by Jiaxin Hu and Xueping Huang PDF
- Proc. Amer. Math. Soc. 136 (2008), 1599-1607 Request permission
Abstract:
We study the following open question raised by Janakiraman in (2006): for $f\in L^1 (\mathbb {R}^n )\cap L^{\infty } (\mathbb {R}^n )$ and $\lambda > 0$, what is the limiting behavior of \[ \left [m\left (\{x \in \mathbb {R}^n :M(|f|^p )(x)>\lambda \}\right )\right ]^{1/p} \] as $p\to \infty$? In this note, we give a complete answer to this question.References
- Juha Heinonen, Lectures on analysis on metric spaces, Universitext, Springer-Verlag, New York, 2001. MR 1800917, DOI 10.1007/978-1-4613-0131-8
- Prabhu Janakiraman, Limiting weak-type behavior for singular integral and maximal operators, Trans. Amer. Math. Soc. 358 (2006), no. 5, 1937–1952. MR 2197436, DOI 10.1090/S0002-9947-05-04097-3
- Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
Additional Information
- Jiaxin Hu
- Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
- Email: hujiaxin@mail.tsinghua.edu.cn
- Xueping Huang
- Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
- Email: hxp@mails.thu.edu.cn
- Received by editor(s): September 3, 2006
- Published electronically: January 3, 2008
- Communicated by: Juha M. Heinonen
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1599-1607
- MSC (2000): Primary 42B25
- DOI: https://doi.org/10.1090/S0002-9939-08-09313-1
- MathSciNet review: 2373589