REPRESENTATION THEOREMS FOR OPERATORS OF TYPE lp,qv,ω,ψ AND Sω,ψ

Let 0 < p, q <= infinity, and Psi : [0,infinity) -> [0, infinity) be a continuous, strictly increasing, subadditive function which satisfies Psi(0) = 0. For sequences v = {v(n)}, omega = {omega(n)} of positive numbers we define sequence classes l(p,q)(v,omega,Psi) and S-omega,S-Psi and give representation theorems for an operator of type l(p,q)(v,omega,Psi) and S-omega,S-Psi.