Consider the general dispersive equation defined bywhere φ（√-△） is a pseudo-differential operator with symbol φ（｜ξ｜）. In this paper, for φ satisfying suitable growth conditions and the radial initial data ...Consider the general dispersive equation defined bywhere φ（√-△） is a pseudo-differential operator with symbol φ（｜ξ｜）. In this paper, for φ satisfying suitable growth conditions and the radial initial data f in Sobolev space, we give the local and global Lq estimate for the maximal operator S; defined by Sφf（x） = sup0〈t〈1｜St,φf（x）｜, where St,φ f is the solution of equation （＊）. These estimates imply the a.e. convergence of the solution of equation （＊）.展开更多
基金The authors would like to express their deep gratitude to the referees for their very careful reading. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11371057, 11471033, 11571160, 11661061）, the Inner Mongolia University Scientific Research Projects （No. NJZZ16234）, and the Natural Science Foundation of Inner Mongolia （No. 2015MS0108）.
文摘Consider the general dispersive equation defined bywhere φ（√-△） is a pseudo-differential operator with symbol φ（｜ξ｜）. In this paper, for φ satisfying suitable growth conditions and the radial initial data f in Sobolev space, we give the local and global Lq estimate for the maximal operator S; defined by Sφf（x） = sup0〈t〈1｜St,φf（x）｜, where St,φ f is the solution of equation （＊）. These estimates imply the a.e. convergence of the solution of equation （＊）.
