We give the L<sup>p</sup>-boundedness for a class of Marcinkiewicz integral operators μΩ, μ<sub>Ω.λ</sub> and μ<sub>Ω.S</sub> related to the Littlewood-Paley g-function, g<...We give the L<sup>p</sup>-boundedness for a class of Marcinkiewicz integral operators μΩ, μ<sub>Ω.λ</sub> and μ<sub>Ω.S</sub> related to the Littlewood-Paley g-function, g<sub>λ</sub><sup>-</sup>function and the area integral S, respectively. These operators have the kernel functions Ω∈H<sup>1</sup>(S<sup>n-1</sup>), the Hardy space on S<sup>n-1</sup>. The results in this paper substantially improve and extend the known results.展开更多
This paper brings forward the concept of generalized H-spaces which extends the concepts of H-spaces and almost probabilistic metric spaces. In this paper, the uniformity and properties far generalized H-space are con...This paper brings forward the concept of generalized H-spaces which extends the concepts of H-spaces and almost probabilistic metric spaces. In this paper, the uniformity and properties far generalized H-space are considered. The conditions of metrization and the form of metric functions for generalized H-spaces, H-spaces and Menger PM-spaces are given and the characteristics of completeness and compactness for generalized H-spaces are presented. The results of this paper generalize and unify some recent results of [1-2, 8, 10].展开更多
基金The first anthor is supported by NSF of China (Grant No. 19971010) DPFIIIF of China and the third anthor is supported in part by NSF Grant DMS 9622979
文摘We give the L<sup>p</sup>-boundedness for a class of Marcinkiewicz integral operators μΩ, μ<sub>Ω.λ</sub> and μ<sub>Ω.S</sub> related to the Littlewood-Paley g-function, g<sub>λ</sub><sup>-</sup>function and the area integral S, respectively. These operators have the kernel functions Ω∈H<sup>1</sup>(S<sup>n-1</sup>), the Hardy space on S<sup>n-1</sup>. The results in this paper substantially improve and extend the known results.
文摘This paper brings forward the concept of generalized H-spaces which extends the concepts of H-spaces and almost probabilistic metric spaces. In this paper, the uniformity and properties far generalized H-space are considered. The conditions of metrization and the form of metric functions for generalized H-spaces, H-spaces and Menger PM-spaces are given and the characteristics of completeness and compactness for generalized H-spaces are presented. The results of this paper generalize and unify some recent results of [1-2, 8, 10].
