Theorems on Strong Riesz Summability Factors

Abstract

Throughout this note it will be assumed that(i) unless otherwise stated, k; is a positive integer,(ii) a ≧ 0; m > − 1,(iii) q ≧ 1; q′ is the conjugate number to q, and is defined by(iv) the functions φ(w), ψ(w) are defined in [0, ∞) with absolutely continuous kth derivatives in every interval [a, W],(v) φ(w) is non-negative and unboundedly increasing,(vi) λ = {λn} is an unboundedly increasing sequence with λ1 > 0.