Fang, Shizan; Nolot, Vincent Sobolev estimates for optimal transport maps on Gaussian spaces. (English) Zbl 1298.49067 J. Funct. Anal. 266, No. 8, 5045-5084 (2014). MSC: 49Q20 35J96 PDFBibTeX XMLCite \textit{S. Fang} and \textit{V. Nolot}, J. Funct. Anal. 266, No. 8, 5045--5084 (2014; Zbl 1298.49067) Full Text: DOI arXiv
Fang, Shizan; Luo, Dejun; Thalmaier, Anton Stochastic differential equations with coefficients in Sobolev spaces. (English) Zbl 1205.60112 J. Funct. Anal. 259, No. 5, 1129-1168 (2010). Reviewer: Iulian Stoleriu (Iaşi) MSC: 60H10 PDFBibTeX XMLCite \textit{S. Fang} et al., J. Funct. Anal. 259, No. 5, 1129--1168 (2010; Zbl 1205.60112) Full Text: DOI arXiv Link
Fang, Shizan; Shao, Jinghai Optimal transport maps for Monge-Kantorovich problem on loop groups. (English) Zbl 1278.90042 J. Funct. Anal. 248, No. 1, 225-257 (2007). MSC: 90B06 90C08 60K30 PDFBibTeX XMLCite \textit{S. Fang} and \textit{J. Shao}, J. Funct. Anal. 248, No. 1, 225--257 (2007; Zbl 1278.90042) Full Text: DOI
Fang, Shizan; Shao, Jinghai Transportation cost inequalities on path and loop groups. (English) Zbl 1068.60013 J. Funct. Anal. 218, No. 2, 293-317 (2005). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 60B15 58J65 PDFBibTeX XMLCite \textit{S. Fang} and \textit{J. Shao}, J. Funct. Anal. 218, No. 2, 293--317 (2005; Zbl 1068.60013) Full Text: DOI
Fang, Shizan Solving stochastic differential equations on \(\text{Homeo}(S^1\)). (English) Zbl 1073.58027 J. Funct. Anal. 216, No. 1, 22-46 (2004), corrigendum 235, No. 2, 721 (2006). Reviewer: Rémi Léandre (Dijon) MSC: 58J65 60H10 34F05 60J60 PDFBibTeX XMLCite \textit{S. Fang}, J. Funct. Anal. 216, No. 1, 22--46 (2004; Zbl 1073.58027) Full Text: DOI
Fang, Shizan Metrics \(\mathcal H_s\) and behaviours as \(s\downarrow \frac {1} {2}\) on loop groups. (English) Zbl 1069.58007 J. Funct. Anal. 213, No. 2, 440-465 (2004). Reviewer: Hans-Bert Rademacher (Leipzig) MSC: 58D05 PDFBibTeX XMLCite \textit{S. Fang}, J. Funct. Anal. 213, No. 2, 440--465 (2004; Zbl 1069.58007) Full Text: DOI
Fang, Shizan Canonical Brownian motion on the diffeomorphism group of the circle. (English) Zbl 1023.60050 J. Funct. Anal. 196, No. 1, 162-179 (2002). Reviewer: J.Franchi (Paris) MSC: 60H07 58J65 58D20 46N50 PDFBibTeX XMLCite \textit{S. Fang}, J. Funct. Anal. 196, No. 1, 162--179 (2002; Zbl 1023.60050) Full Text: DOI
Cruzeiro, Ana Bela; Fang, Shizan Weak Levi-Civita connection for the damped metric on the Riemannian path space and vanishing of Ricci tensor in adapted differential geometry. (English) Zbl 1011.60034 J. Funct. Anal. 185, No. 2, 681-698 (2001). Reviewer: Jacques Franchi (Strasbourg) MSC: 60H07 58J65 58B20 PDFBibTeX XMLCite \textit{A. B. Cruzeiro} and \textit{S. Fang}, J. Funct. Anal. 185, No. 2, 681--698 (2001; Zbl 1011.60034) Full Text: DOI
Fang, Shizan Markovian connection, curvature and Weitzenböck formula on Riemannian path spaces. (English) Zbl 0980.58024 J. Funct. Anal. 181, No. 2, 476-507 (2001). Reviewer: Andrew Bucki (Oklahoma City) MSC: 58J65 58B20 60H07 PDFBibTeX XMLCite \textit{S. Fang}, J. Funct. Anal. 181, No. 2, 476--507 (2001; Zbl 0980.58024) Full Text: DOI
Fang, Shizan Ricci tensors on some infinite dimensional Lie algebras. (English) Zbl 0933.58003 J. Funct. Anal. 161, No. 1, 132-151 (1999). Reviewer: Ya.Belopolskaya (St.Peterburg) MSC: 58B20 17B65 22E65 22E67 58B25 PDFBibTeX XMLCite \textit{S. Fang}, J. Funct. Anal. 161, No. 1, 132--151 (1999; Zbl 0933.58003) Full Text: DOI
Cruzeiro, Ana Bela; Fang, Shizan An \(L^ 2\) estimate for Riemannian anticipative stochastic integrals. (English) Zbl 0867.60030 J. Funct. Anal. 143, No. 2, 400-414 (1997). MSC: 60H05 58J65 PDFBibTeX XMLCite \textit{A. B. Cruzeiro} and \textit{S. Fang}, J. Funct. Anal. 143, No. 2, 400--414 (1997; Zbl 0867.60030) Full Text: DOI
Fang, Shizan; Franchi, Jacques De Rham-Hodge-Kodaira operator on loop groups. (English) Zbl 0901.58067 J. Funct. Anal. 148, No. 2, 391-407 (1997). Reviewer: Yu.E.Gliklikh (Voronezh) MSC: 58J65 60H30 PDFBibTeX XMLCite \textit{S. Fang} and \textit{J. Franchi}, J. Funct. Anal. 148, No. 2, 391--407 (1997; Zbl 0901.58067) Full Text: DOI
Fang, Shizan Stochastic anticipative integrals on a Riemannian manifold. (English) Zbl 0847.58081 J. Funct. Anal. 131, No. 1, 228-253 (1995). Reviewer: S.Eloshvili (Tbilisi) MSC: 58J65 PDFBibTeX XMLCite \textit{S. Fang}, J. Funct. Anal. 131, No. 1, 228--253 (1995; Zbl 0847.58081) Full Text: DOI
Fang, Shizan; Malliavin, Paul Stochastic analysis on the path space of a Riemannian manifold. I: Markovian stochastic calculus. (English) Zbl 0798.58080 J. Funct. Anal. 118, No. 1, 249-274 (1993). Reviewer: S.Eloshvili (Tbilisi) MSC: 58J65 PDFBibTeX XMLCite \textit{S. Fang} and \textit{P. Malliavin}, J. Funct. Anal. 118, No. 1, 249--274 (1993; Zbl 0798.58080) Full Text: DOI