Some Properties of Sobolev Algebras Modelled on Lorentz Spaces

Abstract

In this paper, firstly Lorentz-Sobolev spaces W-L(p,W-q) (k) (R-n) of integer order are introduced and some of their important properties are emphasized. Also, the Banach spaces A(L(pq))(k)(R-n) = L-1-(R-n)boolean AND W-L(p,q)(k) (R-n) (Lorentz-Sobolev algebras in the sense of H.Reiter) are studied. Then, using a result due to H.C.Wang, it is showed that Banach convolution algebras AkL(pq) (Rn) do not have weak factorization. Lastly, it is found that the multiplier algebra of A(L(pq))(k)(R-n) coincides with the measure algebra M (R-n) for 1 < p < infinity and 1 <= q < infinity.