Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-22T21:10:04.390Z Has data issue: false hasContentIssue false
  • English
  • Français

L2(ℝn) boundedness for the commutators of convolution operators

Published online by Cambridge University Press:  22 January 2016

Guoen Hu
Guoen Hu*
Affiliation:
Department of Applied Mathematics, University of Information Engineering, P. O. Box 1001-747, Zhengzhou 450002, People’s Republic of China, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The commutators of convolution operators are considered. By localization and Fourier transform estimates, a sufficient condition such that these commutators are bounded on L2(ℝn) is given. As applications, some new results about the L2(ℝn) boundedness for the commutators of homogeneous singular integral operators are established.

Keywords

42B20
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 163 , September 2001 , pp. 55 - 70
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

References

[1] Alvarez, J., Bagby, R., Kurtz, D. and Pérez, C., Weighted estimates for commutators of linear operators, Studia Math., 104 (1993), 195–209.Google Scholar
[2] Coifman, R., Rochberg, R. and Weiss, G., Factorization theorems for Hardy spaces in several variable, Ann. of Math., 103 (1976), 2611–635.Google Scholar
[3] Coifman, R. and Meyer, Y., Au déla des opérateurs pseudo-différentiles, Astérisque, 57 (1978), 1–185.Google Scholar
[4] Duoandikoetxea, J., Weighted norm inequalities for homogeneous singular integrals, Trans. Amer. Math. Soc., 336 (1993), 869–880.CrossRefGoogle Scholar
[5] Duoandikoetxea, J. and Rubio de Rrancia, J. L., Maximal and singular integrals via Fourier transform estimates, Invent. Math., 84 (1986), 541–561.CrossRefGoogle Scholar
[6] Grafakos, L. and Stefanov, A., Lp bounds for singular integrals and maximal singular integrals with rough kernels, Indiana Univ. Math. J., 47 (1998), 455–469.CrossRefGoogle Scholar
[7] Hu, G., Lu, S. and Ma, B., The commutators of convolution operators (in Chinese), Acta Math. Sinica, 42 (1999), 359–368.Google Scholar
[8] Pérez, C., Endpoint estimates for commutators of singular integral operators, J. Funct. Anal., 128 (1995), 163–185.Google Scholar
[9] Stein, E. M., Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton Univ. Press, Princeton, New Jersey, 1993.Google Scholar