Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T23:34:11.709Z Has data issue: false hasContentIssue false
  • English
  • Français

Criterion of (Lp, Lr) boundedness for a class of multilinear oscillatory singular integrals

Published online by Cambridge University Press:  22 January 2016

Wengu Chen ,
Guoen Hu  and
Shanzhen Lu
Wengu Chen
Affiliation:
Department of Mathematics, Capital Normal University, Beijing 100037, People’s Republic of China
Guoen Hu
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing 100875, People’s Republic of China
Shanzhen Lu
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing 100875, 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.

In this paper, we consider a kind of multilinear operators related to oscillatory singular integrals with rough kernels and give a criterion of certain boundedness for this kind of operators.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 149 , March 1998 , pp. 33 - 51
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

References

[1] Chanillo, S. and Christ, M., Weak (1,1) bounds for oscillatory singular integral Duke Math. J., 55 (1987), 141–155.CrossRefGoogle Scholar
[2] Chen, W., Hu, G. and Lu, S., On a multilinear oscillatory singular integral operator 1, Chinese Annal of Math., 18B (1997), 181–190.Google Scholar
[3] Chen, W., Hu, G. and Lu, S., On a multilinear oscillatory singular integral operator II, Chinese Annal of Math., 18A (1997), 73–82.Google Scholar
[4] Cohen, J. and Gosselin, J., A BMO estimate for multilinear singular integral, Illinois J. of Math., 30 (1986), 445–464.Google Scholar
[5] Cohen, J. and Gosselin, J., On multilinear singular integrals on Rn, Studia Math., 72 (1982), 199–223.Google Scholar
[6] Garcia-Cuerva, J., Harboure, E., Segovia, C. and Torrea, J. L., Weighted norm inequalities for commutators of strongly singular integrals, Indiana Univ. Math. J., 40 (1991), 1397–1420.CrossRefGoogle Scholar
[7] Lu, S. and Zhang, Y., Criterion on Lp-boundedness for a class of oscillatory singular integral with rough kernels, Rev. Mat. Iberoamericana, 8 (1992), 201–219.Google Scholar
[8] Ricci, F. and Stein, E. M., Harmonic analysis on nilpotent groups and singular integrals I. oscillatory integral, J. Funct. Anal., 73 (1987), 179–194.Google Scholar
[9] Stein, E. M., Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, New Jersey, 1970.Google Scholar