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Displaying similar documents to “Some Tauberian theorems for Euler and Borel summability.”

Tauberian theorems for Cesàro summable double integrals over ℝ + 2

Ferenc Móricz (2000)

Studia Mathematica

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Given ⨍ ∈ L l 1 o c ( ℝ + 2 ) , denote by s(w,z) its integral over the rectangle [0,w]× [0,z] and by σ(u,v) its (C,1,1) mean, that is, the average value of s(w,z) over [0,u] × [0,v], where u,v,w,z>0. Our permanent assumption is that (*) σ(u,v) → A as u,v → ∞, where A is a finite number. First, we consider real-valued functions ⨍ and give one-sided Tauberian conditions which are necessary and sufficient in order that the convergence (**) s(u,v) → A as u,v → ∞ follow from (*). Corollaries allow these...