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Volume 8 |Article ID 405313 | https://doi.org/10.1155/2010/405313

Z. T. Abdikalikova, A. A. Kalybay, "Summability of a Tchebysheff system of functions", Journal of Function Spaces, vol. 8, Article ID 405313, 16 pages, 2010. https://doi.org/10.1155/2010/405313

Summability of a Tchebysheff system of functions

Z. T. Abdikalikova1 and A. A. Kalybay2

1L.N. Gumilyev Eurasian National University, Munaytpasov st., 5, 010008 Astana, Kazakhstan

2Kazakhstan Institute of Management, Economics and Strategic Research, Abai ave., 4, 050010 Almaty, Kazakhstan

Academic Editor: Pankaj Jain
Received01 Aug 2008

Abstract

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.

Copyright © 2010 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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