Journal of Function Spaces

Journal of Function Spaces / 2010 / Article

Open Access

Volume 8 |Article ID 405313 | 16 pages | https://doi.org/10.1155/2010/405313

Summability of a Tchebysheff system of functions

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)=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.

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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