A Bilinear Fractional Integral on Compact Lie Groups

Abstract

As an analog of a well-known theorem on the bilinear fractional integral on 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.

Rough bilinear fractional integrals with variable kernels

“…The operators K 1,α and B 1,α were well studied in [6,8]. Some transference results of B 1,α on the n-torus were also obtained in [2] (see also [3] for a version on a compact Lie group). On the other hand, the study of the operators K Ω,α (as well as B Ω,α ) and its related operators with rough Ω were recently attracted several authors (see [4,13]).…”

Weighted estimates for bilinear fractional integral operator on the Heisenberg group

“…We would like to mention the work [Kai14] where fractional integral operators are extended in the more general context of spaces of homogeneous type, and also the article [CF11] where the authors have treated an analogue of Kenig and Stein's bilinear fractional integral operator on compact Lie groups. Motivated by the above discussion, let us define bilinear fractional integral operator on H n .…”

Central oscillating multipliers on compact Lie groups

“…Motivated by these observations, this paper fills some of these gaps on compact Lie groups. A compact Lie group is a natural extension of the torus, and it has many similarities with Euclidean space that allow us to obtain more precise results in harmonic analysis (see [2,3,[9][10][11]). On the other hand, such an extension is nontrivial.…”