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Journal of the Ramanujan Mathematical Society

Volume 30, Issue 4, December 2015  pp. 361–373.

A note on weighted Sobolev algebras Lω1 (Rd) ∩ Wkp (Rd)

Authors:  Nihan Güngör and Birsen Sagir
Author institution:Gümüshane University, Faculty of Engineering, Department of Mathematical Engineering, 29100 Gümüshane/Turkey

Summary:  Let 1 ≤ p < ∞ and ω be Beurling's weight function on Rd. In~this article, we demonstrate some harmonic properties of Sobolev space Wkp (Rd) which consists of all functions on Rd whose weak derivatives up to and including order k belong to Lp (Rd). Also, we deal with some harmonic properties of intersection space Ak,ωp (Rd) = Lω1 (Rd) ∩ Wkp (R d) by aid of Beurling algebra Lω1 (Rd) and Sobolev space Wkp (Rd). Finally, we research the inclusions and continuous embeddings between the spaces A k, ω p (Ω) where Ω ⊂ Rd be open set.

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