On multipliers in weighted Sobolev spaces. Part I - L.Kussainova, L.; Myrzagaliyeva, A. (Вестник Карагандинского университета, 2016)
Let X, Y be Banach spaces whose elements are functions y : Ω → R. We say that a function z : Ω → R is a pointwise multiplier on the pair (X, Y ), if T x = zx ∈ Y and the operator T : X → Y is bounded. M (X → Y ) denotes the multiplier space on the pair (X, Y ). We introduce the norm lz; M (X → Y )l = lT ; X → Y l in M (X → Y ). Let 1 ≤ p < ∞. Let m be an integer. W m denotes the weighted Sobolev space with m 1/p 1/p the finite norm lulW m p,ω0 ,ω1 l = lω0 |∇mu|lLp + lω1 ulLp,v . The aim of this work is to obtain descriptions of multiplier spaces for the pair of weighted Sobolev spaces (W l q,ω0 ,ω1 ).
Keywords: weighted Sobolev space; pointwise multiplier