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deLeeuw’s theorem on Littlewood-Paley functions

  • Chang-Pao Chen (a1), Dashan Fan (a2) and Shuichi Sato (a3)

Abstract

We establish certain deLeeuw type theorems for Littlewood-Paley functions. By these theorems, we know that the boundedness of a Littlewood-Paley function on ℝn is equivalent to the boundedness of its corresponding Littlewood-Paley function on the torus Tn.

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References

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[DFP] Ding, Y.,Fan, D. and Pan, Y., On Littlewood-Paley functions and singular integrals, Hokkaido Math. J, 29 (2000), 537552.
[F] Fan, D., Multipliers on certain function spaces, Rend. Mat. Palermo, Tomo XLIII (1994), 449463.
[FS1] Fan, D. and Sato, S., Transference on certain multilinear multiplier operators, J. Aust. Mth. Soc., 70 (2001), 3755.
[FS2] Fan, D. and Sato, S., Weak type (1, 1) estimates for Marcinkiewicz integrals with rough kernels, Tohoku Math. J., 53 (2001), 265284.
[K] Kaneko, M., Boundedness of some operators composed of Fourier multipliers, Tôhoku Math. J. (2), 35 (1983), 267288.
[KS] Kaneko, M. and Sato, E., Notes on transference of continuity from maximal Fourier multiplier operators on n to those on n , Interdiscip. Inform. Sci, 4 (1998), 97107.
[KT] Kenig, C. and Tomas, P., Maximal operators defined by Fourier multiplier, Studia Math., 68 (1980), 7983.
[L] deLeeuw, K., On Lp multiplier, Ann. of Math., 91 (1965), 364379.
[LL] Liu, Z. and Lu, S., Transference and restriction of maximal multiplier operators on Hardy spaces, Studia Math., 105 (1993), 121134.
[Sa1] Sato, S., Remarks on square functions in the Littlewood-Paley theory, Bull. Austral. Math. Soc., 58 (1998), 199211.
[Sa2] Sato, S., Multiparameter Marcinkiewicz integrals and a resonance theorem, The Bull. of Faculty of Education, Kanazawa University, 48 (1999), 121.
[SW] Stein, E.M. and Weiss, G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, 1971.
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Keywords

deLeeuw’s theorem on Littlewood-Paley functions

  • Chang-Pao Chen (a1), Dashan Fan (a2) and Shuichi Sato (a3)

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