Marcinkiewicz Integrals on Weighted Weak Hardy Spaces
We prove that, under the condition Ω∈Lipα, Marcinkiewicz integral μΩ is bounded from weighted weak Hardy space WHwpRn to weighted weak Lebesgue space WLwpRn for maxn/n+1/2,n/n+α<p≤1, where w belongs to the Muckenhoupt weight class. We also give weaker smoothness condition assumed on Ω to imply th...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/765984 |
| Summary: | We prove that, under the condition Ω∈Lipα, Marcinkiewicz integral μΩ is bounded from weighted weak Hardy space WHwpRn to weighted weak Lebesgue space WLwpRn for maxn/n+1/2,n/n+α<p≤1, where w belongs to the Muckenhoupt weight class. We also give weaker smoothness condition assumed on Ω to imply the boundedness of μΩ from WHw1ℝn to WLw1Rn. |
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| ISSN: | 2314-8896 2314-8888 |