加权Sobolev空间的完备性

ON THE COMPLETENESS OF THE WEIGHTED SOBOLEV SPACE

本文研究加权Soblev空间完备性 .我们运用Ap 权的构造性质证明 ,当 1<p <q <+∞时 ,有ω∈Aq,使得W1,p(ωdx)是不完备的 ,从而证明了当 1<p <+∞时 ,使得W1,p(ωdx)完备的最佳加权条件是ω(x)∈Ap.

In this paper we consider the completeness of the weighted Sobolev space. An example is constructed to show that for 1<p<q<+∞ there exists ω∈A q such that W 1,p(ωdx) is incomplete. Therefore the best weighted condition for the completeness of the weighted Sobolev space W 1,p(ωdx) is ω(x)∈A p.