主要研究的具体问题: 1.多线性算子的有界性与最佳估计:几何不等式(HLS不等式),Brascamp-Lieb不等式，Fourier乘子等；2.极大算子的最佳估计3.算子的离散化及乘子的周期化,乘子转移定理的最佳常数等。
主持项目:
1.浙江省自然科学基金青年项目 LQ18A010002，Hardy-Littlewood-Sobolev不等式最佳常数的研究, 2018.01-2021.12,已结题。
2.国家自然科学基金青年项目 12001488,积分不等式的离散化：最佳常数和极值函数问题, 2021.01- 2023.12
主要科研成果:
1.Wu Di, Shi Zuoshunhua, Yan Dunyan*, Sharp constants in the doubly weighted Hardy-Littlewood-Sobolev inequality, Science China Mathematics,May 2014 Vol. 57 No. 5: 963–970.
2. Wu Di, Yan Dunyan*, Sharp constants for a class of multilinear integral operators and some applications, Science China Mathematics, 2016, 59 (5) : 907-920.
3. Zuoshunhua Shi, Wu Di and Dunyan Yan, On the Multilinear Fractional Integral Operators with Correlation Kernels,Journal of Fourier Analysis and Applications, 2017, 1-50.
4. Di Wu, Zuoshunhua Shi, Xudong Nie, Dunyan Yan*, On a k-Fold Beta Integral Formula, The Journal of Geometric Analysis(2020)30:4240–4267.
5. Di Wu, Dunyan Yan*, Continuity of Hardy-Littlewood maximal function, Acta Mathematicae Applicatae Sinica, English Series, Vol. 36, No. 4 (2020) 982–990.
