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
Let (H, B, u) be an abstract Wiener space. New spaces of test functionals and distributions having kernels of the chaos decomposition in (Hn,n>0) are constructed. Their counterparts over Rm are completely character...Let (H, B, u) be an abstract Wiener space. New spaces of test functionals and distributions having kernels of the chaos decomposition in (Hn,n>0) are constructed. Their counterparts over Rm are completely characterized in terms of the H-transform.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Let (H, B, u) be an abstract Wiener space. New spaces of test functionals and distributions having kernels of the chaos decomposition in (Hn,n>0) are constructed. Their counterparts over Rm are completely characterized in terms of the H-transform.
