Sobolev Type Spaces Based on Lorentz-Karamata Spaces

Abstract

In this paper, firstly Lorentz-Karamata-Sobolev spaces Wk<inf>L(p;q;b)</inf> (ℝn) of integer order are introduced and some of their important properties are emphasized. Also, Banach spaces Ak<inf>L(p;q;b)</inf> (ℝn) = L1 (ℝn) ∩ Wk<inf>L(p;q;b)</inf> (ℝn) (Lorentz-Karamata-Sobolev algebras) are studied. Using a result of H.C. Wang, it is showed that Banach convolution algebras Ak<inf>L(p;q;b)</inf> (ℝn) don’t have weak factorization and the multiplier algebra of Ak L(p;q;b) (Rn) coincides with the measure algebra M(ℝn) for 1 < p < 1 and 1 ≤ q < ∞. © 2016, University of Nis. All rights reserved.