Sobolev Type Spaces Based on Lorentz-Karamata Spaces

Abstract

In this paper, firstly Lorentz-Karamata-Sobolev spaces W-L(p,q;b)(k) (R-n) of integer order are introduced and some of their important properties are emphasized. Also, Banach spaces A(L(p,q;b))(k) (R-n) = L-1 (R-n) boolean AND W-L(p,q;b)(k) (R-n) (Lorentz-Karamata-Sobolev algebras) are studied. Using a result of H.C.Wang, it is showed that Banach convolution algebras A(L(p,q;b))(k) (R-n) don't have weak factorization and the multiplier algebra of A(L(p,q;b))(k) (R-n) coincides with the measure algebra M(R-n) for 1 < p < infinity and 1 <= q < infinity.