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| Hausdorff Operators on Function Spaces |
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Citation： |
Jiecheng CHEN,Dashan FAN,Jun LI.Hausdorff Operators on Function Spaces[J].Chinese Annals of Mathematics B,2012,33(4):537~556 |
| Page view： 2353
Net amount： 1734 |
Authors： |
Jiecheng CHEN; Dashan FAN; Jun LI; |
Foundation： |
the National Natural Science Foundation of China (Nos. 10931001, 10871173). |
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| Abstract： |
The authors mainly study the Hausdorff operators on Euclidean space \ $ \mathbb{R} ^{n}$. They establish boundedness of the Hausdorff operators in various function spaces, such as Lebesgue spaces, Hardy spaces, local Hardy spaces and Herz type spaces. The results reveal that the Hausdorff operators have better performance on the Herz type Hardy spaces $H\dot{K}_{q}^{\alpha ,p}(\mathbf{ \mathbb{R} }^{n})$ than their performance on the Hardy spaces $H^{p}(\mathbf{ \mathbb{R} }^{n})$ when $0 |
Keywords： |
Hausdorff operator, Hardy operator, Hardy space, Herz space |
Classification： |
42B25, 42B30 |
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