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Volume 10, Issue 3, Article 78 |
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On Certain Rough Integral Operators and Extrapolation
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Authors: |
Hussain Al-Qassem, Leslie Cheng, Yibiao Pan, |
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Keywords:
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Maximal operator, Rough kernel, Singular integral, Orlicz spaces, Block spaces, Extrapolation, $L^p$ boundedness. |
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Date Received:
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24/01/2009 |
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Date Accepted:
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31/08/2009 |
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Subject Codes: |
Primary 42B20; Secondary 42B15, 42B25.
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Editors: |
Sever S. Dragomir, |
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Abstract: |
In this paper, we obtain sharp  estimates of two classes of maximal operators related to rough singular integrals and Marcinkiewicz integrals These estimates will be used to obtain similar estimates for the related singular integrals and Marcinkiewicz integrals. By the virtue of these estimates and extrapolation we obtain the boundedness of all the aforementioned operators under rather weak size conditions. Our results represent significant improvements as well as natural extensions of what was known previously.
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