On Singular Integrals with Cauchy Kernel on Weight Subspaces: The Basicity Property of Sines and Cosines Systems in Weight Spaces
A singular operator with Cauchy kernel on the subspaces of weight Lebesgue space is considered. A sufficient condition for a bounded action of this operator from a subspace to another subspace of weight Lebesgue space of functions is found. These conditions are not identical with Muckenhoupt conditi...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/717501 |
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| Summary: | A singular operator with Cauchy kernel on the subspaces of weight Lebesgue space is
considered. A sufficient condition for a bounded action of this operator from a subspace
to another subspace of weight Lebesgue space of functions is found. These conditions are
not identical with Muckenhoupt conditions. Moreover, the completeness, minimality, and
basicity of sines and cosines systems are considered. |
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| ISSN: | 0161-1712 1687-0425 |