学术报告（范大山 11.18）

摘要：

In this talk we discuss a maximal oscillating multiplier operator T*_{α, β}, 0<α<1, on an n-dimensional (n≥2) compact connected manifold (M,g) without boundary. We prove that T*_{α, β} is bounded from Hardy spaces Hᴾ(M) to Lᴾ(M), 0<p<1, if and only if |1/2-1/p|≤β/(nα). We also obtain that T*_{α, β} is bounded from L¹(M) to L^{1,∞}(M)  if β>(nα)/2. All results are even new on Rⁿ. These results are analogues of some well-known theorems by Wainger, Fefferman-Stein, Sjölin and Miyachi.

This talk is based on Joint works with Jiecheng Chen, Fayou Zhao and Ziyao Liu.