Abstract
The L 2(ℝn) boundedness for the multilinear singular integral operators defined by
is considered, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, A has derivatives of order one in BMO(ℝn). A sufficient condition based on the Fourier transform estimate and implying the L 2(ℝn) boundedness for the multilinear operator T A is given.
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Cohen, J.: A sharp estimate for a multilinear singular integral on ℝn. Indiana Univ. Math. J., 30(2), 693–702 (1981)
Hu, G.: A sharp function estimate for the multilinear singular integral operators. Approx. and its Appl., 16(1), 17–25 (2000)
Hofmann, S.: On Certain non-standard Calderón-Zygmund operators. Studia Math., 109(2), 105–131 (1994)
Pérez, C.: Endpoint estimate for commutators of singular integral operators. J. Funct. Anal., 128(1), 163–185 (1995)
Hofmann, S.: Weighted norm inequalities for commutators of rough singular integrals. Indiana Univ. Math. J., 39(4), 1275–1304 (1990)
Hu, G.: L 2 boundedness for the commutators of convolution operators. Nagoya Math. J., 163, 55–70 (2001)
Grafakos, L., Stefanov, A.: L p bounds for singular integrals and maximal singular integrals with rough kernels. Indiana Univ. Math. J., 47(2), 455–469 (1998)
Han, Y., Sawyer, E. T.: Para accretive functions, the weak boundedness propertiy and the Tb theorem. Rev. Mat. Iberoamericana, 6(1), 17–41 (1990)
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Supported by the NSF of China, Grant No. 19701039
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Hu, G.E. L 2(ℝn) Boundedness for a Class of Multilinear Singular Integral Operators. Acta Math Sinica 19, 397–404 (2003). https://doi.org/10.1007/s10114-002-0231-5
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DOI: https://doi.org/10.1007/s10114-002-0231-5