Summability of a Tchebysheff system of functions
We consider a special type of Tchebysheff systems of functions {ui(⋅)}in=0 and {Vi(⋅)}in=0 defined on the intervals (0, 1] and [1,+∞), respectively, such that ui(t)=tα0∫t1t1α1∫t11t2α2…∫ti−11tiαidtidti−1…dt1 and ui(t)=tβ0∫1tt1β1∫1t1t2β2…∫1ti−1tiβidtidti−1…dt1. We find necessary and sufficient conditi...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2010/405313 |
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| Summary: | We consider a special type of Tchebysheff systems of functions {ui(⋅)}in=0 and {Vi(⋅)}in=0 defined on the intervals (0, 1] and [1,+∞), respectively, such that ui(t)=tα0∫t1t1α1∫t11t2α2…∫ti−11tiαidtidti−1…dt1 and ui(t)=tβ0∫1tt1β1∫1t1t2β2…∫1ti−1tiβidtidti−1…dt1. We find necessary and sufficient conditions under which functions from the investigated systems belong to the corresponding Lebesgue spaces Lp(0, 1) and Lp(1,+∞). In order to prove the main results we obtain lower and upper estimates of these functions that are of independent interest. |
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| ISSN: | 0972-6802 |