Plancherel-Pôlya type inequality on spaces of homogeneous type and its applications
Plancherel-Pôlya type inequality on spaces of homogeneous type and its applications
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DOI：
10.1090/s0002-9939-98-04445-1
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
Y.-S. Han
中科院分区：
文献类型：
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作者：
Y.-S. Han
本文利用作者得到的齐型空间上的离散Calderon再生公式，得到了齐型空间上的PlancherelP6lya型不等式。这些不等式给出了作者和E.T.Sawyer早些时候引入的齐型Besov空间IP‘i和’Riebel-Lizorkin空间F‘qon空间的新刻画，并允许我们将这些空间推广到p，q<；1的情形。此外，利用这些不等式，我们可以很容易地证明齐型空间上的Littlewood-Paley G-函数和S-函数是等价的，这给出了Macias和Segovia引入的齐型空间上Hardy空间的一个新的刻画。
In this paper, using the discrete Calderon reproducing formula on spaces of homogeneous type obtained by the author, we obtain the PlancherelP6lya type inequalities on spaces of homogeneous type. These inequalities give new characterizations of the Besov spaces ip'I and the 'riebel-Lizorkin spaces F'qon spaces of homogeneous type introduced earlier by the author and E. T. Sawyer and also allow us to generalize these spaces to the case where p, q < 1. Moreover, using these inequalities, we can easily show that the Littlewood-Paley G-function and S-function are equivalent on spaces of homogeneous type, which gives a new characterization of the Hardy spaces on spaces of homogeneous type introduced by Macias and Segovia.