In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on...In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on the geometrical properties of the Banach space in which the martingales take values.展开更多
The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0〈r≤1. ...The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0〈r≤1. Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.展开更多
In this article, we establish some atomic decomposition theorems for martin- gale Hardy-Lorentz spaces. As applications, with the help of weak atomic decompositions, some interpolation theorems for martingale Hardy-Lo...In this article, we establish some atomic decomposition theorems for martin- gale Hardy-Lorentz spaces. As applications, with the help of weak atomic decompositions, some interpolation theorems for martingale Hardy-Lorentz spaces are proved.展开更多
In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms. They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory. And then three atomic deco...In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms. They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory. And then three atomic decomposition theorems for martingales in weak martingale Hardy spaces are proved. With the help of the weak atomic decompositions of martingale, a sufficient condition for a sublinear operator defined on the weak martingale Hardy spaces to be bounded is given. Using the sufficient condition, we obtain a series of martingale inequalities with respect to the weak Lp-norm, the inequalities of weak (p ,p)-type and some continuous imbedding relationships between various weak martingale Hardy spaces. These inequalities are the weak versions of the basic inequalities in the classical martingale Hp-theory.展开更多
In this paper an atomic decomposition theorem for Banach-space-valued weak Hardy regular martingale space wpHα^s（X） is given. As an application, p-smoothable Banach spaces are characterized in terms of bounded subl...In this paper an atomic decomposition theorem for Banach-space-valued weak Hardy regular martingale space wpHα^s（X） is given. As an application, p-smoothable Banach spaces are characterized in terms of bounded sublinear operators defined on Banach-space-valued weak Hardy regular martingale space wpHa^s（X）. Keywords Martingale, weak Hardy space, atomic decomposition, p-smoothable Banach space展开更多
基金Supported by the National Natural Foundation of China(10671147)
文摘In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on the geometrical properties of the Banach space in which the martingales take values.
基金Supported by the National Natural Science Foun-dation of China (10371093)
文摘The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0〈r≤1. Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.
基金supported by the National Natural Science Foundation of China(10871016)
文摘In this article, we establish some atomic decomposition theorems for martin- gale Hardy-Lorentz spaces. As applications, with the help of weak atomic decompositions, some interpolation theorems for martingale Hardy-Lorentz spaces are proved.
基金This work was supported by National Natural Science Foundation of China (Grant No. 10371093).
文摘In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms. They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory. And then three atomic decomposition theorems for martingales in weak martingale Hardy spaces are proved. With the help of the weak atomic decompositions of martingale, a sufficient condition for a sublinear operator defined on the weak martingale Hardy spaces to be bounded is given. Using the sufficient condition, we obtain a series of martingale inequalities with respect to the weak Lp-norm, the inequalities of weak (p ,p)-type and some continuous imbedding relationships between various weak martingale Hardy spaces. These inequalities are the weak versions of the basic inequalities in the classical martingale Hp-theory.
基金Supported by National Natural Science Foundation of China （Grant No. 10671147）
文摘In this paper an atomic decomposition theorem for Banach-space-valued weak Hardy regular martingale space wpHα^s（X） is given. As an application, p-smoothable Banach spaces are characterized in terms of bounded sublinear operators defined on Banach-space-valued weak Hardy regular martingale space wpHa^s（X）. Keywords Martingale, weak Hardy space, atomic decomposition, p-smoothable Banach space
