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On non-uniqueness of the order of saturation (II)

Published online by Cambridge University Press:  24 October 2008

B. Kuttner
B. Kuttner
Affiliation:
University of Birmingham
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Extract

1. In this paper, the notation and terminology of [2] will be used throughout. As in [2], we consider the space of bounded measurable functions of period 2π, with the sup norm. We let K0ρ denote the subspace consisting of those functions in the space considered which have the further property that the conjugate function belongs to Lrρ 1. Again as in [2], we consider regular summability methods given by a sequence-to-sequence matrix transformation D = (dnk), where

and where, for fixed n,

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 1 , July 1984 , pp. 115 - 117
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

[1] Kuttner, B., Mohapatra, R. N. and Sahney, B. N.. Saturation results for a class of linear operators. Math. Proc. Cambridge Philos Soc. 94 (1983), 133–148.CrossRefGoogle Scholar
[2] Kuttner, B. and Sahney, B. N.. On non-uniqueness of the order of saturation. Math. Proc. Cambridge Philos. Soc. 84, (1978), 113–116.CrossRefGoogle Scholar
[3] Sunouchi, Q. and Watari, C.. On determination of the class of saturation in the theory of approximation of functions II. Tohoku Math. J. (2) 11 (1959), 480–488.CrossRefGoogle Scholar