Composition operators are used to study the E(p,q) spaces. The boundedness of these operators is also considered. The criteria for these operators to be bounded are given in terms of the Carleson measure.
We prove that for any p perfect set of positive measure and for it＇s any density point x0 one can construct a measurable function f（x）, bounded on [0,1）, such that each measurable and bounded function, which coinc...We prove that for any p perfect set of positive measure and for it＇s any density point x0 one can construct a measurable function f（x）, bounded on [0,1）, such that each measurable and bounded function, which coincides with f（x） on the set p has diverging Fourier-Walsh series on the point xo.展开更多
Let （X, d, μ） be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2（X）. Assume that the semigroup e-^tL gen...Let （X, d, μ） be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2（X）. Assume that the semigroup e-^tL generated by -L satisfies the Gaussian upper bounds on L2（X）. In this article we study a local version of Hardy space hi （X） associated with L in terms of the area function characterization, and prove their atomic characters. Furthermore, we introduce a Moser type local boundedness condition for L, and then we apply this condition to show that the space hzL（X） can be characterized in terms of the Littlewood-Paley function. Finally, a broad class of applications of these results is described.展开更多
文摘This paper presents a method of generating new set-valued measure from a family of bounded set-valued measure,especially from bounded vector measures.
文摘Composition operators are used to study the E(p,q) spaces. The boundedness of these operators is also considered. The criteria for these operators to be bounded are given in terms of the Carleson measure.
文摘We prove that for any p perfect set of positive measure and for it＇s any density point x0 one can construct a measurable function f（x）, bounded on [0,1）, such that each measurable and bounded function, which coincides with f（x） on the set p has diverging Fourier-Walsh series on the point xo.
基金supported by China Postdoctoral Science Foundation funded project(Grant No.201104383)the Fundamental Research Funds for the Central Universities(Grant No.11lGPY56)+1 种基金National Natural Science Foundation of China(Grant No.10925106)Guangdong Province Key Laboratory of Computational Science and Grant for Senior Scholars from the Association of Colleges and Universities of Guangdong
文摘Let （X, d, μ） be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2（X）. Assume that the semigroup e-^tL generated by -L satisfies the Gaussian upper bounds on L2（X）. In this article we study a local version of Hardy space hi （X） associated with L in terms of the area function characterization, and prove their atomic characters. Furthermore, we introduce a Moser type local boundedness condition for L, and then we apply this condition to show that the space hzL（X） can be characterized in terms of the Littlewood-Paley function. Finally, a broad class of applications of these results is described.
