Abstract:
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
= lu; Wp,ω ,ω l = lω0 |∇mu|lLp + lω1 ulLp,v . The aim of this work is to
p,ω0 ,ω1 0 1
obtain descriptions of multiplier spaces for the pair of weighted Sobolev spaces (W l
m q,ω0 ,ω1
) in the
case 1 ≤ q < p < ∞.
