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Sobolev type spaces based on Lorentz-Karamata spaces

Eryilmaz İlker (aOndokuz Mayıs University, Faculty of Sciences and Arts, Department of Mathematics, Kurupelit, Samsun-TURKEY)

In this paper, firstly Lorentz-Karamata-Sobolev spaces Wk,(p,q,b) (Rn) of integer order are introduced and some of their important properties are emphasized. Also, Banach spaces Ak,L(p,q,b)(Rn) = L1(Rn)∩ Wk,L(p,q,b)(Rn) (Lorentz-Karamata-Sobolev algebras) are studied. Using a result of H.C.Wang, it is showed that Banach convolution algebras AkL(p,q,b)(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 < 1.

Keywords: Slowly varying function, Lorentz-Karamata space, Sobolev space, FP􀀀algebra, weak factorization