Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T06:58:34.607Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Theorems on Strong Nörlund Summability

Published online by Cambridge University Press:  20 November 2018

Frank P. Cass
Frank P. Cass*
Affiliation:
University of Western Ontario, London, Ontario
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Throughout this paper H, H1 etc. will denote positive constants which will not necessarily be the same at different occurrences. If is a series, we shall use the notation For a real, define

1

Let {pn} be a sequence with p0>0 and pn≥0 for n > 0. Define

2

The following identities are immediate:

3

4

where

5

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 1 , March 1972 , pp. 63 - 69
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Borwein, D., On strong and absolute summability, Proc. Glasgo. Math. Assoc. 4 (1960), 122-139.Google Scholar
2. Borwein, D. and Cass, F. P., Strong Norlund summability, Math. Z. 103 (1968), 94-111.Google Scholar
3. Borwein, D. and Cass, F. P., Multiplication theorems for strong Nörlund summability, Math. Z. 107 (1968), 33-42.Google Scholar
4. Cass, F. P., Convexity theorems for Nörlund and strong Nörlund summability, Math. Z. 112 (1969), 357-363.Google Scholar
5. Flett, T. M., Some remarks on strong summability, Quart. J. Math. Oxford Ser. 10 (1959), 115-139.Google Scholar
6. Garabedian, H. L. and Randels, W. C., Theorems on Reisz means,Duke Math. J. 4 (1938), 529-533.Google Scholar
7. Hardy, G. H., Divergent series, Oxford, 1949.Google Scholar
8. Hardy, G. H. and Littlewood, J. E., Some properties of fractional integrals I, Math. Z. 27 (1928), 565-606.Google Scholar
9. Hardy, G. H., Littlewood, J. E., and Pölya, G., The maximum of a certain bilinear form, Proc. London Math. Soc. (2) 25 (1926), 265-282.Google Scholar
10. Hardy, G. H., Littlewood, J. E., and Pölya, G., Inequalities, Cambridge, 1934.Google Scholar
11. Kuttner, B. and Thorpe, B., On the strong Nörlund summability of a Cauchy product series, Math. Z. 111 (1969), 69-86.Google Scholar
12. Wilansky, A., Functional analysis, Blaisdell, Waltham, Mass., 1964.Google Scholar