QK Spaces on the Unit Circle
We introduce a new space QK(∂D) of Lebesgue measurable functions on the unit circle connecting closely with the Sobolev space. We obtain a necessary and sufficient condition on K such that QK(∂D)=BMO(∂D), as well as a general criterion on weight functions K1 and K2, K1≤K2, such that QK1(∂D)QK2(∂D)....
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/234790 |
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| Summary: | We introduce a new space QK(∂D) of Lebesgue measurable functions on the unit circle connecting closely with the Sobolev space. We obtain a necessary and sufficient condition on K such that QK(∂D)=BMO(∂D), as well as a general criterion on weight functions K1 and K2, K1≤K2, such that QK1(∂D)QK2(∂D). We also prove that a measurable function belongs to QK(∂D) if and only if it is Möbius bounded in the Sobolev space LK2(∂D). Finally, we obtain a dyadic characterization of functions in QK(∂D) spaces in terms of dyadic arcs on the unit circle. |
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| ISSN: | 2314-8896 2314-8888 |