Tauberian Constants for Some Double Hausdorff Matrices
DOI:
https://doi.org/10.5644/SJM.13.1.02Keywords:
Double series, double Hausdorff matrices, Tauberian constantsAbstract
Mirza and Thorpe [9], obtained the Tauberian constant for $C(1, 1)$ summability for sequences satisfying the boundedness condition $(m^2 + n^2)a_{mn} = O(1)$. In this paper we investigate the analogous questions for double Hausdorff matrices.
Downloads
References
C. R. Adams, Hausdorff transformations for double sequences, Bull. Amer. Math. Soc., 39 (1933), 303--312.
Hubert Delange, Theoremes tauberiens pour les series multiples de Dirichlet et les integrales multiples de Laplace, Ann. Sci. Ecole Norm. Sup., 70 (3) (1953), 51 -103.
G. H. Hardy, Notes on some points in the integral calculus, $XXXII:$ On double series and double integrals, Messenger Math., 41 (1912), 44--48.
G. H. Hardy, Divergent Series, Oxford University Press (1949).
A. Jakimovski, Tauberian constants for Hausdorff transformations, Bull. Res. Council Israel Sect. F 9F (1961), 175--184.
A. Jakimovski and D. Leviatan, A property of approximation operators and applications to Tauberian constants, Math. Zeit., 102 (1967), 177--204.
H. D. Kloosterman, Tauberian theorems for Cesáro summability of double series, Proc. Akad. Wet. Amsterdam, 43 (1940), 215--223.
K. Knopp, Llimitierung-Umkehrsätz für Doppelfolgen, Math. Zeit., 45 (1939), 573--589.
M. Y. Mirza and B. Thorpe, Tauberian constants for double series, J. London Math. Soc., 57 (1998), 170--182.
