Study of harmonic analysis and applications to partial differential equations

新井研究调和分析负弯曲流形。设M是一个完备的单连通黎曼流形，其截面曲率K_M满足-∞ < -k^2_2 [小于或等于] K_M [小于或等于] -k^2_1 < 0，其中k_1和k_2为正常数。Arai得到了M上椭圆调和函数的几个结果。特别是他建立的基本部分调和分析M证明定理有关的哈代空间，BMO，VMO，Carleson措施，绿色的潜力。作为应用，他还研究了布洛赫函数理论的流形和正则性问题的退化调和措施。Ozawa用真实的变量方法研究了非线性薛定谔方程、非线性波动方程和非线性Krein-Gordon方程。Yajima得到了薛定谔方程基本解的一些结果。Kanjin证明了Jacobi展开的Paley不等式，并研究了Hausdorff算子作用于真实的哈代空间.

Arai studied harmonic analysis on negatively curved manifolds. Let M be a complete, simply connected Riemannian manifold whose sectional curvatures K_M satisfy -∞ < -k^2_2 【less than or equal】 K_M 【less than or equal】 -k^2_1 < 0, where k_1 and k_2 are positive constants. Arai obtained several results on elliptic harmonic functions on M. In particular he established fundamental part of harmonic analysis on M by proving theorems related to Hardy spaces, BMO, VMO, Carleson measures, Green's potential. As applications, he also studied Bloch function theory on manifolds and the regularity problem of degenerate harmonic measures. Ozawa studied by using real variable method nonlinear Schrodinger equations, nonlinear wave equations and nonlinear Krein-Gordon equations. Yajima obtained some results on the fundamental solutions of Schrodinger equations. Kanjin proved Paley's inequality for Jacobi expansions and studied the Hausdorff operator acting on real Hardy spaces.