A Problem on Normed Köthe Spaces

Abstract

Let L^ρ denote a complete normed Köthe space, K a nonnegative, Lebesgue-measurable function on (0,∞) × (0,∞) which is homogeneous of degree γ (γ ∊ ℝ), and

$$(Kf)(t): = \int_0^\infty {K(t,s)f(s)ds\quad (f \in {L^\rho },t > 0)}$$

((1))

.