Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-05-19T02:59:22.526Z Has data issue: false hasContentIssue false

Lp Estimates for Multilinear Operators of Strongly Singular Integral Operators*

Published online by Cambridge University Press:  11 January 2016

Junfeng Li
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, Chinajunfli@yahoo.com.cn
Shanzhen Lu
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, Chinalusz@bnu.edu.cn
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, the authors get the Lp estimates for the commutators generated by strongly singular integral operators and BMO functions and the corresponding multilinear operators by the scale changing method introduced by Carleson and Sjölin.

Keywords

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2006

Footnotes

*

This research was supported by the National 973 project of China (Grant. No. G19990751).

To whom correspondence should be addressed. E-mail: lusz@bnu.edu.cn

References

[ABKP] Alvarez, J., Bagay, R. J., Kurtz, D. S. and Pérez, C., Weighted estimates for commutators of linear operators, Studia Math., (2) 104 (1993), 195209.Google Scholar
[C1] Chanillo, S., A note on commutators, Indiana Univ. Math. J., 31 (1982), 716.Google Scholar
[C2] Chanillo, S., Weighted norm inequality for strongly singular convolution operators, Trans. Amer. Math. Soc., 281 (1984), 77107.Google Scholar
[CG] Cohen, J. and Gosselin, J., A BMO estimate for multilinear singular integrals, Illinois J. Math., 30 (1986), 445464.Google Scholar
[CRW] Coifman, R. R., Rochberg, R. and Weiss, G., Fractorization theorems for Hardy spaces in several variable, Ann. of Math., 103 (1976), 611625.Google Scholar
[CS] Carleson, L. and Sjölin, P., Oscillatory integrals and a multiplier problem for the disc, Studia Math., 44 (1972), 287299.Google Scholar
[F] Fefferman, C., Inequality for strongly singular convolution operators, Acta Math., 124 (1970), 936.Google Scholar
[GHST] Garcia-Cuerva, J., Harboure, E., Segovia, C. and Torrea, J. L., Weighted norm inequalities for commutators of strongly singular integrals, Ind. Univ. Math. J., (4) 40 (1991), 13971420.Google Scholar
[Hi] Hirschman, I. I., On multiplier transformations, Duke Math. J., 26 (1959), 221242.Google Scholar
[HL] Hu, G. E. and Lu, S. Z., The commutators of the Bochner-Riesz operator, Tôhoku Math., 124 (1996), 259266.Google Scholar
[Hu] Hu, Y., On multilinear fractional integrals, Approximation Theory and Its Applications, 3 (1985), 3351.Google Scholar
[LL] Li, J. F. and Lu, S. Z., The boundedness of multilinear operators of strongly singular integral operators on Hardy spaces, Progress in Nature Science (China), 15 (2005), 1016.Google Scholar
[Sj] Sjölin, P., Lp estimate for strongly singular convolution operators in ℝn , Ark. Math., 14 (1976), 5964.Google Scholar
[St] Stein, E. M., Harmonic Analysis: Real-variable Methods, Orthogonality and Oscillatory Integrals, Princeton Univ. Press, Princeton, N. J., 1993.Google Scholar