ABSTRACT. In this small note, we will characterize the boundedness, compactness and closedness of the range of the multiplication operators on LorentzKaramata-Bochner spaces L p,q;b (Ω, X) for p, q ∈ (0, ∞].

The boundedness, compactness and closedness of the range of weighted composition operators acting on weighted Lorentz spaces L(p, q, wdµ) for 1 < p ≤ ∞, 1 ≤ q ≤ ∞ are characterized.

In this paper, two new classes of subalgebras of L 1 (G) generated by Lorentz-Karamata spaces are investigated and some fundamental properties of these spaces are examined. Also, the multipliers space (homomorphisms space) on L 1 (G) ∩ L (p, q; b) (G) spaces are characterized.

Bu çalışmada Lebesgue uzayları üzerinde tanımlı bir operatörün bileşke operatör olması için gerekli şartlar ve bileşke operatörlerinin sağladığı bazı özelliklerin gösterilmesi amaçlanmaktadır.

Let G be a locally σ−compact abelian group with Haar measure. In this paper, firstly, weighted Lorentz-Karamata L w p,q;b (G) spaces will be defined and examined with some fundamental properties. Next, we will establish some criteria for noncompactness of embedding theorems for weighted Lorentz-Karamata (WLK) spaces.