堯小華，男，漢族，1974年4月13日生於.江西臨川。
基本介紹
- 中文名：堯小華
- 民族：漢族
- 出生日期：1974年4月13日
- 出生地：江西臨川
學歷,所授課程,研究興趣與主題,代表論文,
學歷
1998年本科畢業於華中理工大學數學系；.
2001年碩士畢業於華中科技大學數學系；
2004年博士畢業於蘭州大學數學系；
1998.7-2003.10 任華中科技大學數學系助教、講師；
2004.3-2004.5 美國Rutgers University訪問學者；
200310-2009.7 任華中師範大學數學與統計學學院副教授；
2009.7-至今 任華中師範大學數學與統計學學院教授；
2008.2-2008.7 北京師範大學數學科學學院訪問學者；
2009.9-2009.12 北京套用物理與計算數學研究所訪問教授；
2011.3-2012.3 美國Johns Hopkins University 高級訪問學者；
2011.3 入選2010年教育部新世紀優秀人才計畫。
所授課程
1.實變函式 (本科)
2.泛函分析 (本科)
3.線性偏微分運算元分析 (研究生)
4.調和分析引論 (研究生)
5.無界運算元理論 (研究生) 等。
研究興趣與主題
主要集中在調和分析與偏微分運算元的交叉領域，具體包括如下幾個主題：
1.振盪積分與色散方程的色散估計；
2.微分運算元相關的調和分析問題的研究；
3.Schrödinger 型運算元研究等。
代表論文
1. Zheng Q., Yao X. and Fan D., Convex hypersurfaces and Lp estimates for Schrödinger equations. Journal of Functional Analysis. 208(2004), 122-139.
2. Zheng Q., Li L., Yao X., and Fan D., The Spectrum of differential operators in Hp spaces. Illinois Journal of Math. 49(2005),45-62
3. Yao X., Zheng Q., Oscillatory integrals and Lp Estimates for Schrödinger Equations. Journal of Differential Equation, 244(2008), 741-752.
4. Zheng Q., Yao X., Higher-Order Kato Class Potentials for Schrödinger operators. Bulletin of London Math. Soc., 41(2009), 293-301.
5. Ding Y., Yao X., Lp－Lq Estimates for dispersive Equations and related applications. J. Math. Anal. Appl., 356( 2009), 711-728.
6. Ding Y., Yao X., Hp－Hq Estimates for dispersive Equations and related applications. Journal of Functional Analysis , 257 (2009) 2067–2087
7. Kim J., Arnold, A. Yao X. , Global estimates of fundamental solutions for higher-order Schrödinger equations. Monatshefte für Mathematik, online, 2011
8. Deng Q., Yao X., Lp－Lq estimates for a class of pseudodifferential equations and its applications.Acta Mathematica Sinica, English Series , Jul., 2011, Vol. 27, No. 7, pp. 1435–1448.
9. Chen W, Miao C, Yao X., Dispersive estimates with geometry of finite type. Communication in Partial Differential Equations. 37: 479–510, 2012
10. Deng Q, Ding Y， Yao，X., Hardy spaces associated with higher-order divergence eilliptic operator. Journal of Functional Analysis，263(2012), 604-674
11. A. Arnold, J. Kim and X. Yao, Estimates for a class of oscillatory integrals and decay rates for wave-type equations. J. Math. Anal. Appl. 394 (2012) 139–151
12. Peng Shao, Xiaohua Yao, Uniform Sobolev resolvent estimates for Laplace-Beltrami operators on compact manifolds. To appear in International Mathematics Research Notices.(IMRN)
13. Chao Deng, Xiaohua Yao, Well-posedness and ill-posedness of 3D-incompressible generalized Navier-Stokes equations in Triebel-Lizorkin spaces,
To appear in Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
14. Deng Q, Ding Y， Yao，X., Remarks on the form core asscociated with higher order Schrodinger operators. To appear in Indiana University Math. J.
15. J.Bourgain, P. Shao, C. Sogge, X.Yao On $L^p$-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds. To appear in Communications in Mathematical Physics
16. A. Sikora, Linxin Yan，Xiaohua Yao, On the boundedness of spectral multipliers for operators with generalized Gaussian estimates, J. Functional Analysis, 266 (2014) 368–409
17. Deng Q, Ding Y， Yao，X., Riesz transform associated to higher order Schrodinger type operators. Preprint.
18. Deng Q, Ding Y， Yao，X., BMO and VMO spaces associated with higher-order divergence eilliptic operators. Preprint.
19. Deng Q, Ding Y， Yao，X., The pointwise estimates of heat kernel of higher order Schrodinger type semigroups. Submitted
20. Chao Deng, Xiaohua Yao, Ill -posedness of 3D-incompressible Navier-Stokes equations in Triebel-Lizorkin spaces, Submitted
