| Fractional Type Marcinkiewicz Integral on Hardy Spaces |
| Received:May 21, 2009 Revised:July 13, 2009 |
| Key Words:
fractional type Marcinkiewicz Integral Herz type Hardy space Hardy space.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.10861010; 10871024). |
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| Abstract: |
| The authors in the paper proved that if $\Omega$ is homogeneous of degree zero and satisfies some certain logarithmic type Lipschitz condition, then the fractional type Marcinkiewicz Integral $\mu_{\Omega , \alpha}$ is an operator of type ($H\dot{K}^{n(1-1/q_{1}),p}_{q_{1}},\dot{K}^{n(1-1/q_{1}),p}_{q_{2}}$) and of type ($H^{1}(R^{n}),L^{n/(n-\alpha)}$). |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.02.006 |
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