Abstract
The authors prove the certain de Leeuw type theorems on some non-convolution operators, and give some applications on certain known results.
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References
de Leeuw, K., On L p multiplier, Ann. of Math., 91, 1965, 364–379.
Stein, E. M. and Weiss, G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, 1971.
Kenig, C. and Thomas, P., Maximal operators defined by Fourier multiplier, Studia Math., 68, 1980, 79–83.
Auscher, P. and Carro, M. J., On relations between operators on ℝn, \( \mathbb{T} \) n and ℤn. Studia Math., 101, 1992, 165–182.
Fan, D., Multipliers on certain function spaces, Circolo Matematico Di Palermo., Tomo XLIII, 1994, 449–463.
Kaneko, M. and Sato, E., Notes on transference of continuity from maximal Fourier multiplier operators on R n to those on T n. Interdiscip. Inform. Sci., 4, 1998, 97–107.
Liu, Z. and Lu, S., Transference and restriction of maximal multiplier operators on Hardy spaces, Studia Math., 105, 1993, 121–134.
Chen, D. and Fan, D., Multiplier transformations on H p spaces, Studia Math., 131, 1998, 189–204.
Fan, D. and Sato, S., Transference on certain multilinear multiplier operators, J. Austral. Math. Soc., 70, 2001, 37–55.
Lacey, M. and Thiele, C., L p estimates on the bilinear Hilbert transform, Ann. of Math., 146(2), 1997, 693–724.
Calderón, A. P. and Zygmund, A., On singular integrals with variable kernels, Applicable Anal., 7, 1977/1978, 221–238.
Hu, G. and Lu, S., The commutator of the Bochner-Riesz operator, Tohoku Math J., 48, 1996, 259–266.
Chen, Y. and Ding, Y., L 2 boundedness for commutators of rough singular integral with variable kernel, Rev. Math. Ibe., 24, 2008, 531–547.
Pérez, C. and Torres, R., Sharp maximal function estimates for multilinear singular integral operators, Contemp. Math., 320, 2003, 323–331.
Stein, E. M., Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, 1970.
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Project supported by the National Natural Science Foundation of China (Nos. 10931001 and 10871173), the Educational Science Foundation of Zhejiang (No. Z201017584) and the Science Foundation of Zhejiang University of Science and Technology (No. F501108A02).
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Zhang, Y., Fan, D. & Chen, J. Transference on some non-convolution operators from euclidean spaces to torus. Chin. Ann. Math. Ser. B 32, 59–68 (2011). https://doi.org/10.1007/s11401-010-0624-1
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DOI: https://doi.org/10.1007/s11401-010-0624-1