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Journal of Function Spaces and Applications
Volume 8, Issue 1, Pages 87-102
http://dx.doi.org/10.1155/2010/405313

Summability of a Tchebysheff system of functions

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

Received 1 August 2008

Academic Editor: Pankaj Jain

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.

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)=tα0t1t1α1t11t2α2ti11tiαidtidti1dt1 and ui(t)=tβ01tt1β11t1t2β21ti1tiβidtidti1dt1. 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.