We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob＇s inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey sp...We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob＇s inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob＇s inequality on martingale block spaces, we obtain the Davis＇ decompositions for martingale Morrey spaces.展开更多
在齐型空间(X,d,μ)中,假设L是L^(2)(X)上的一个非负自伴算子,其热核满足Gauss上、下界估计.给定N个具有一致估计的Hörmander型谱乘子m_(i),1 i N,本文应用Doob变换和Chang-Wilson-Wolff对二进鞅平方函数的exp(L^(2))估计,建立极...在齐型空间(X,d,μ)中,假设L是L^(2)(X)上的一个非负自伴算子,其热核满足Gauss上、下界估计.给定N个具有一致估计的Hörmander型谱乘子m_(i),1 i N,本文应用Doob变换和Chang-Wilson-Wolff对二进鞅平方函数的exp(L^(2))估计,建立极大函数sup1≤i≤N|m_(i)(L)f|的L^(p)有界性,并给出L^(p)有界的最佳的上界估计√log(1+N).基于这个估计,本文给出乘子m的一类充分条件,其极大函数M_(m,L)f(x)=sup_(t>0)|m(t L)f(x)|在L^(p)(X)上是有界的.展开更多
文摘We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob＇s inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob＇s inequality on martingale block spaces, we obtain the Davis＇ decompositions for martingale Morrey spaces.
文摘在齐型空间(X,d,μ)中,假设L是L^(2)(X)上的一个非负自伴算子,其热核满足Gauss上、下界估计.给定N个具有一致估计的Hörmander型谱乘子m_(i),1 i N,本文应用Doob变换和Chang-Wilson-Wolff对二进鞅平方函数的exp(L^(2))估计,建立极大函数sup1≤i≤N|m_(i)(L)f|的L^(p)有界性,并给出L^(p)有界的最佳的上界估计√log(1+N).基于这个估计,本文给出乘子m的一类充分条件,其极大函数M_(m,L)f(x)=sup_(t>0)|m(t L)f(x)|在L^(p)(X)上是有界的.
