On absolute generalized Norlund summability of double orthogonal series

Krasniqi, X. Z.

doi:10.22075/ijnaa.2010.96

On absolute generalized Norlund summability of double orthogonal series

Document Type : Research Paper

Author

X. Z. Krasniqi

Department of Mathematics and Computer Sciences, University of Prishtina Avenue "Mother Theresa " 5, Prishtin\"e, 10000, KOSOV\"{E}

10.22075/ijnaa.2010.96

Abstract

In the paper [Y. Okuyama, On the absolute generalized Norlund summability of orthogonal series, Tamkang J. Math. Vol. 33, No. 2, (2002), 161-165] the author has found some sufficient conditions under which an orthogonal series is summable $|N,p,q|$ almost everywhere. These conditions are expressed in terms of coefficients of the series. It is the purpose of this paper to extend this result to double absolute summability $|N^{(2)},\mathfrak{p},\mathfrak{q}|_k$, $(1\leq k\leq 2)$.

Keywords

Double orthogonal series

Double Norlund summability