In this paper, we study certain Hausdorff operators in the high-dimensional product spaces. We obtain their power weighted boundedness from Lp to Lq and characterize the necessary and sufficient conditions for their b...In this paper, we study certain Hausdorff operators in the high-dimensional product spaces. We obtain their power weighted boundedness from Lp to Lq and characterize the necessary and sufficient conditions for their boundedness on the power weighted Lp spaces. Moreover, in the case p = q, we obtain the sharp bound constants.展开更多
Let M be a a-finite yon Neumann algebra and let 9i C M be a maximal subdiagonal algebra with respect to a faithful normal conditional expectation Ф. Based on the Haagerup＇s noncommutative Lp space LP（M） associated...Let M be a a-finite yon Neumann algebra and let 9i C M be a maximal subdiagonal algebra with respect to a faithful normal conditional expectation Ф. Based on the Haagerup＇s noncommutative Lp space LP（M） associated with M, we consider Toeplitz operators and the Hilbert transform associated with 8i. We prove that the commutant of left analytic Toeplitz algebra on noncommutative Hardy space H2（A4） is just the right analytic Toeplitz algebra. Furthermore, the Hilbert transform on noncommutative LP（Yt4） is shown to be bounded for 1 （ p （ ce. As an application, we consider a noncomnmtative analog of the space BMO and identify the dual space of noncommutative Hl（M） as a concrete space of operators.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11271330 and 10931001)Education Foundation of Zhejiang Province(Grant No.Y201225707)Natural Science Foundation of Zhejiang Province of China(Grant No.Y604563)
文摘In this paper, we study certain Hausdorff operators in the high-dimensional product spaces. We obtain their power weighted boundedness from Lp to Lq and characterize the necessary and sufficient conditions for their boundedness on the power weighted Lp spaces. Moreover, in the case p = q, we obtain the sharp bound constants.
基金supported by National Natural Science Foundation of China(Grant No.11371233)the Fundamental Research Funds for the Central Universities(Grant No.GK201301007)
文摘Let M be a a-finite yon Neumann algebra and let 9i C M be a maximal subdiagonal algebra with respect to a faithful normal conditional expectation Ф. Based on the Haagerup＇s noncommutative Lp space LP（M） associated with M, we consider Toeplitz operators and the Hilbert transform associated with 8i. We prove that the commutant of left analytic Toeplitz algebra on noncommutative Hardy space H2（A4） is just the right analytic Toeplitz algebra. Furthermore, the Hilbert transform on noncommutative LP（Yt4） is shown to be bounded for 1 （ p （ ce. As an application, we consider a noncomnmtative analog of the space BMO and identify the dual space of noncommutative Hl（M） as a concrete space of operators.
