BOUNDEDNESS OF HIGHER ORDER COMMUTATORS OF GENERALIZED FRACTIONAL INTEGRAL OPERATORS ON HARDY SPACES

Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-type Hardy spaces.  

Self-similar solutions to the hyperbolic mean curvature flow

This article concerns the self-similar solutions to the hyperbolic mean curvature flow (HMCF) for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity.  

具有局部时间分数阶导数的非线性Zoomeron方程的精确解

利用R. Khalil所提出的分数阶导数概念,研究具有局部时间分数阶导数的非线性Zoomeron方程,得到该方程行波解所满足方程的相图和分支. 同时运用指数函数展开和首次积分方法,可以得到Zoomeron方程的包括孤立波解、周期解等各类行波解的精确解析表达式.