Transference on some non-convolution operators from euclidean spaces to torus

Yandan Zhang , Dashan Fan , Jiecheng Chen

Chinese Annals of Mathematics, Series B ›› 2011, Vol. 32 ›› Issue (1) : 59 -68.

PDF
Chinese Annals of Mathematics, Series B ›› 2011, Vol. 32 ›› Issue (1) : 59 -68. DOI: 10.1007/s11401-010-0624-1
Article

Transference on some non-convolution operators from euclidean spaces to torus

Author information +
History +
PDF

Abstract

The authors prove the certain de Leeuw type theorems on some non-convolution operators, and give some applications on certain known results.

Keywords

n-Torus / de Leeuw’s theorem / Commutator

Cite this article

Download citation ▾
Yandan Zhang, Dashan Fan, Jiecheng Chen. Transference on some non-convolution operators from euclidean spaces to torus. Chinese Annals of Mathematics, Series B, 2011, 32(1): 59-68 DOI:10.1007/s11401-010-0624-1

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

de Leeuw K.. On L p multiplier. Ann. of Math., 1965, 91: 364-379

[2]

Stein E. M., Weiss G.. Introduction to Fourier Analysis on Euclidean Spaces, 1971, Princeton: Princeton University Press

[3]

Kenig C., Thomas P.. Maximal operators defined by Fourier multiplier. Studia Math., 1980, 68: 79-83

[4]

Auscher P., Carro M. J. O. r. b. o. o. ℝ.. Studia Math., 1992, 101: 165-182

[5]

Fan D.. Multipliers on certain function spaces. Circolo Matematico Di Palermo., 1994, TomoXLIII: 449-463

[6]

Kaneko M., Sato E.. Notes on transference of continuity from maximal Fourier multiplier operators on R n to those on T n. Interdiscip. Inform. Sci., 1998, 4: 97-107

[7]

Liu Z., Lu S.. Transference and restriction of maximal multiplier operators on Hardy spaces. Studia Math., 1993, 105: 121-134

[8]

Chen D., Fan D.. Multiplier transformations on H p spaces. Studia Math., 1998, 131: 189-204

[9]

Fan D., Sato S.. Transference on certain multilinear multiplier operators. J. Austral. Math. Soc., 2001, 70: 37-55

[10]

Lacey M., Thiele C.. L p estimates on the bilinear Hilbert transform. Ann. of Math., 1997, 146(2): 693-724

[11]

Calderón A. P., Zygmund A.. On singular integrals with variable kernels. Applicable Anal., 1977, 7: 221-238

[12]

Hu G., Lu S.. The commutator of the Bochner-Riesz operator. Tohoku Math J., 1996, 48: 259-266

[13]

Chen Y., Ding Y.. L 2 boundedness for commutators of rough singular integral with variable kernel. Rev. Math. Ibe., 2008, 24: 531-547

[14]

Pérez C., Torres R.. Sharp maximal function estimates for multilinear singular integral operators. Contemp. Math., 2003, 320: 323-331

[15]

Stein E. M.. Singular Integrals and Differentiability Properties of Functions, 1970, Princeton: Princeton University Press

AI Summary AI Mindmap
PDF

119

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/