Frontiers of Mathematics in China >

2011 , Vol. 6 >Issue 3: 427 - 447

DOI: https://doi.org/10.1007/s11464-011-0114-0

RESEARCH ARTICLE

Maximal operators of commutators of Bochner-Riesz means with Lipschitz functions

  • Shuli GONG 1 ,
  • Bolin MA , 2
Expand
  • 1. College of Mathematics and Economtrics, Hunan University, Changsha 410082, China
  • 2. College of Science and Information Engineering, Jiaxing University, Jiaxing 314001, China

Received date: 13 Aug 2010

Accepted date: 19 Feb 2011

Published date: 01 Jun 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
Fold

Abstract

This paper presents a weighted L2 estimate with power weights for the maximal operator of commutators generated by compactly supported multipliers and Lipschitz functions. As an application, we study the almost convergence of the commutators, which is generated by the Bochner-Riesz means under the critical index and Lipschitz functions, for functions in Lp (p≥2).

Key words： Maximal operator; commutator; Bochner-Riesz means; Lipschitz function

Cite this article

Shuli GONG , Bolin MA . Maximal operators of commutators of Bochner-Riesz means with Lipschitz functions[J]. Frontiers of Mathematics in China, 2011 , 6(3) : 427 -447 . DOI: 10.1007/s11464-011-0114-0

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Alvarez J, Bagby R J, Kurtz D S and Pérez C. Weighted estimates for commutators of linear operators. Studia Math, 1993, 104: 195-209

2
Carbery A, Rubio de Francia J L, Vega L. Almost everywhere summability of Fourier integrals. J London Math Soc, 1988, 38: 513-524

3
Chanillo S. A note on commutators. Indiana Univ Math J, 1982, 31: 7-16

DOI

4
Cordoba A. The Kakeya maximal function and the spherical summation multiplier. Amer J Math, 1977, 99: 1-22

DOI

5
Hoffman S. Weighted norm inequalities and vector-valued inequalities for certain rough operators. Indiana Univ Math J, 1993, 42: 1-14

DOI

6
Hu G, Lu S. The commutator of the Bochner-Riesz operator. Tôhoku Math J, 1996, 48: 259-266

7
Hu G, Lu S. The maximal operator associated with the commutator of the Bochner-Riesz operator. Beijing Math, 1996, 2: 96-106

8
Hu G, Lu S. A weighted L2 estimates for the commutator of the Bochner-Riesz operator. Proc Amer Math Soc, 1997, 125: 2867-2873

DOI

9
Liu Z. The Lipschitz estimates for the maximal commutator of the Bochner-Riesz operator. J. Beijing Normal Univ (Natural Science Edition), 2002, 38: 160-164

10
Ma B, Hu G. Maximal operators associated with commutators of spherical means. Tohoku Math J, 1998, 50: 349-363

DOI

11
Paluszynski M. Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss. Indiana Univ Math J, 1995, 44: 1-17

DOI

12
Shi X, Sun Q. Weighted norm inequalities for Bochner-Riesz operators and singular integral operators. Proc Amer Math Soc, 1992, 116: 665-673

DOI

13
Stein E M. Harmonic Analysis: Real-Variable Methods, Orthogonolity and Oscillatory Integrals. Princeton: Princeton Univ Press, 1993

14
Xia X. Boundedness of some singular integral operators and their commutators. <DissertationTip/> Thesis, Beijing Normal Univ, 2007

Options
Outlines

/

〈 〉