On Weighted <inline-formula> <graphic file="1029-242X-2010-485705-i1.gif"/></inline-formula> Integrability of Functions Defined by Trigonometric Series
<p/> <p>We introduce a new class of sequences called <inline-formula> <graphic file="1029-242X-2010-485705-i2.gif"/></inline-formula> and give a sufficient and necessary condition for weighted <inline-formula> <graphic file="1029-242X-2010-485705...
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2010/485705 |
| Summary: | <p/> <p>We introduce a new class of sequences called <inline-formula> <graphic file="1029-242X-2010-485705-i2.gif"/></inline-formula> and give a sufficient and necessary condition for weighted <inline-formula> <graphic file="1029-242X-2010-485705-i3.gif"/></inline-formula> integrability of trigonometric series with coefficients to belong to the above class. This is a generalization of the result proved by M. Dyachenko and S. Tikhonov (2009). Then we discuss the relations among the weighted best approximation and the coefficients of trigonometric series. Moreover, we extend the results of B. Wei and D. Yu (2009) to the class <inline-formula> <graphic file="1029-242X-2010-485705-i4.gif"/></inline-formula>.</p> |
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| ISSN: | 1025-5834 1029-242X |