A Bilinear Fractional Integral on Compact Lie Groups
Canadian mathematical bulletin, Tome 54 (2011) no. 2, pp. 207-216

Voir la notice de l'article provenant de la source Cambridge University Press

As an analog of a well-known theoremon the bilinear fractional integral on ${{\mathbb{R}}^{n}}$ by Kenig and Stein, we establish the similar boundedness property for a bilinear fractional integral on a compact Lie group. Our result is also a generalization of our recent theorem about the bilinear fractional integral on torus.
DOI : 10.4153/CMB-2010-096-9
Mots-clés : 43A22, 43A32, 43B25, bilinear fractional integral, Lp spaces, Heat kernel
Chen, Jiecheng; Fan, Dashan. A Bilinear Fractional Integral on Compact Lie Groups. Canadian mathematical bulletin, Tome 54 (2011) no. 2, pp. 207-216. doi: 10.4153/CMB-2010-096-9
@article{10_4153_CMB_2010_096_9,
     author = {Chen, Jiecheng and Fan, Dashan},
     title = {A {Bilinear} {Fractional} {Integral} on {Compact} {Lie} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {207--216},
     year = {2011},
     volume = {54},
     number = {2},
     doi = {10.4153/CMB-2010-096-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-096-9/}
}
TY  - JOUR
AU  - Chen, Jiecheng
AU  - Fan, Dashan
TI  - A Bilinear Fractional Integral on Compact Lie Groups
JO  - Canadian mathematical bulletin
PY  - 2011
SP  - 207
EP  - 216
VL  - 54
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-096-9/
DO  - 10.4153/CMB-2010-096-9
ID  - 10_4153_CMB_2010_096_9
ER  - 
%0 Journal Article
%A Chen, Jiecheng
%A Fan, Dashan
%T A Bilinear Fractional Integral on Compact Lie Groups
%J Canadian mathematical bulletin
%D 2011
%P 207-216
%V 54
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-096-9/
%R 10.4153/CMB-2010-096-9
%F 10_4153_CMB_2010_096_9

[1] [1] Clerc, J. L., Bochner-Riesz means of Hp functions (0 < p < 1) on compact Lie groups. In: Noncommutative harmonic analysis and Lie groups (Marseille-Luminy, 1985), Lecture Notes in Math., 1234, Springer, Berlin, 1987, pp. 86–107. Google Scholar

[2] [2] Chen, J. and Fan, D., Some bilinear estimates. J. Korean Math. Soc. 46(2009), no. 3, 609–620. doi:10.4134/JKMS.2009.46.3.609 Google Scholar

[3] [3] Cowling, M., Mantero, A. M., and Ricci, F., Pointwise estimates for some kernels on compact Lie groups. Rend. Circ. Mat. Palerma 31(1982), no. 2, 145–158. doi:10.1007/BF02844350 Google Scholar

[4] [4] Fan, D., Calderón-Zygmund operators on compact Lie groups. Math Z. 216(1994), no. 3, 401–415. doi:10.1007/BF02572330 Google Scholar

[5] [5] Janson, S., On interpolation of multilinear operators. In: Function spaces and applications (Lund, 1986), Lecture Notes in Math., 1302, Springer, Berlin, 1988, pp. 290–302. Google Scholar

[6] [6] Kenig, C. and Stein, E. M., Multilinear estimates and fractional integration. Math. Res. Lett. 6(1999), no. 1, 1–15. Google Scholar

[7] [7] Stein, E. M., Topics in harmonic analysis related to the Littlewood-Paley theory. Annals of Mathematics Studies, 63, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1970 Google Scholar

[8] [8] Zheng, X. A., Riesz and Bessel transformations on compact Lie groups. Kexue Tongbao (English Ed.) 32(1987), no. 24, 1657–1663. Google Scholar

Cité par Sources :