On a class of multilinear oscillatory singular integral operators

Guoen HU; Shanzhen LU; Dachun YANG

doi:10.2969/jmsj/05030623

Guoen HU, Shanzhen LU, Dachun YANG

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Keywords: multilinear operator, oscillatory singular integral, BMO

JOURNAL FREE ACCESS

1998 Volume 50 Issue 3 Pages 623-637

DOI https://doi.org/10.2969/jmsj/05030623

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Published: 1998 Received: April 01, 1996 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: KEYWORD Details: Right : multilinear operator, oscillatory singular integral, BMO

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) S. Chanillo, Weighted norm inequalities for strongly singular convolution operators, Trans. Amer. Math. Soc. 281 (1984), 77-107.
2) S. Chanillo, D. Kurtz and G. Sampson, Weighted weak (1,1) and the weighted L^p estimate for oscillating kernels, Trans. Amer. Math. Soc. 295 (1986), 127-145.
3) W. Chen, G. Hu and S. Lu, On a multilinear oscillatory singular integral operator (II), Chin. J. of Contemporary Math., 18 (1997), 31-42.
4) J. Cohen, A sharp estimate for a multilinear singular integral in Rⁿ, Indiana Univ. Math. J. 30 (1981), 693-702.
5) J. Cohen and J. Gosselin, A BMO estimate for multilinear singular integrals, Illinois J. of Math. 30 (1986), 445-464.
6) D. Fan and Y. Pan, Boundedness of certain oscillatory singular integrals, Studia Math. 114 (1995), 106-116.
7) C. Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9-36.
8) C. Fefferman and E. M. Stein, H^p spaces of several variables, Acta Math. 129 (1972), 137-193.
9) S. Hofmann, On certain nonstandard Calderón-Zygmund operators, Studia Math. 109 (1994), 105-131.
10) P. Sjölin, Convolution with oscillating kernels on H^p spaces, J. London Math. Soc. 23 (1981), 442-454.

Right : [1] S. Chanillo, Weighted norm inequalities for strongly singular convolution operators, Trans. Amer. Math. Soc. 281 (1984), 77-107.
[2] S. Chanillo, D. Kurtz and G. Sampson, Weighted weak (1, 1) and the weighted L^p estimate for oscillating kernels, Trans. Amer. Math. Soc. 295 (1986), 127-145.
[3] W. Chen, G. Hu and S. Lu, On a multilinear oscillatory singular integral operator (II), Chin. J. of Contemporary Math., 18 (1997), 31-42.
[4] J. Cohen, A sharp estimate for a multilinear singular integral in Rⁿ, Indiana Univ. Math. J. 30 (1981), 693-702.
[5] J. Cohen and J. Gosselin, A BMO estimate for multilinear singular integrals, Illinois J. of Math. 30 (1986), 445-464.
[6] D. Fan and Y. Pan, Boundedness of certain oscillatory singular integrals, Studia Math. 114 (1995), 106-116.
[7] C. Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9-36.
[8] C. Fefferman and E. M. Stein, H^p spaces of several variables, Acta Math. 129 (1972), 137-193.
[9] S. Hofmann, On certain nonstandard Calderón-Zygmund operators, Studia Math. 109 (1994), 105-131.
[10] P. Sjölin, Convolution with oscillating kernels on H^p spaces, J. London Math. Soc. 23 (1981), 442-454.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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