摘要：  In this report, we use interpolation and iterative methods to study the fractional integral operator FΩ,α with variable kernel. We obtain the sharp size condition on Ω to ensure the (Lq,Lp) boundedness of FΩ,α for 0< α < n, 1 < p < ∞. We also obtain some corresponding estimates of the rough bilinear fractional integral. By Fourier transform estimates and a method of approximation, we prove that the commutator FΩ,α,b, which is generated by FΩ,α with a function b ∈ n+2α CMO(Rn), is compact from L 2n (Rn) to L2(Rn).

.

 

报告人：  郑涛涛，浙江科技学院理学院调和分析研究团队成员。2015年获浙江大学理学博士学位，主要研究方向为PDE与调和分析技术、奇异积分算子的有界性。相关结果已在Electron. J. Differential Equations, Ann. Funct. Anal., J. Funct. Spaces等国内外数学杂志发表。