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Lacunary theorems for Cesàro means

Published online by Cambridge University Press:  24 October 2008

B. Kuttner  and
I. J. Maddox
B. Kuttner
Affiliation:
University of Birmingham and Queen's University, Belfast
I. J. Maddox
Affiliation:
University of Birmingham and Queen's University, Belfast
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Extract

Suppose that (ni) = (n1, n2,…) and (mi) are infinite sequences of positive integers with ni < mi < ni+1. It is well-known and easily proved that, if a series σak is (C, 1) summable to s and has lacunae (ni, mi) such that ak = 0 (ni < k < mi) with

then where

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 2 , March 1983 , pp. 231 - 235
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

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