On absolute generalized Norlund summability of double orthogonal series

Document Type : Research Paper


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


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 $|N^{(2)},\mathfrak{p},\mathfrak{q}|_k$, $(1\leq k\leq 2)$.


Volume 2, Issue 2 - Serial Number 2
December 2011
Pages 62-74
  • Receive Date: 11 January 2011
  • Revise Date: 21 May 2011
  • Accept Date: 29 May 2010