Summability of a Tchebysheff system of functions

Abdikalikova, Z. T.; Kalybay, A. A.

doi:https://doi.org/10.1155/2010/405313

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 L_p(0, 1) and L_p(1,+∞). In order to prove the main results we obtain lower and upper estimates of these functions that are of independent interest.

Copyright

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.

Journal of Function Spaces

Summability of a Tchebysheff system of functions

Abstract

Copyright