Inversion theorems for the Riesz method of summation of double series (Q1187322)

Let \(p\) and \(q\) be two non-negative real numbers; let \(\{\lambda_k\}\) and \(\{\mu_k\}\) be two strictly (to \(\infty\)) increasing non-negative sequences. Bivariate Riesz-summation of a double sequence \(\{u_{k\ell}\}\) concerns \((x>0,\;y>0)\) \[ R(x,y)=x^{-p}y^{-q}\sum_{\lambda_k<x,\;\mu_\ell<y}(x-\lambda_k)^p(y-\mu_\ell)^q u_{k\ell}. \] The authors prove a Tauberian theorem and a high indices theorem for this bivariate summability method.