On One Extension Theorem Dealing With Weighted Orlicz-Slobodetskii Space. Analysis On Lipschitz Subgraph And Lipschitz Domain

Having a given weight rho(x) = tau(dist(x, partial derivative Omega)) defined on Lipschitz boundary domain Omega and an Orlicz function Psi, we construct the subordinated weight omega(.,.) defined on partial derivative Omega x partial derivative Omega and extension operator Ext(L) : Lip(partial derivative Omega) bar right arrow Lip(Omega) form Lipschitz functions defined on. Omega to Lipschitz functions defined on (Omega) over bar, independent of tau and Psi, in such a way that Ext(L) extends to the bounded operator from the subspace of weighted Orlicz-Slobodetskii space Y-omega(Psi,Psi) (partial derivative Omega) generated by Lipschitz functions and subordinated to the weight. to Orlicz-Sobolev space W-rho(1,Psi) (Omega). More detailed analysis on Lipschitz subgraph is also provided. Result is new in the unweighted Orlicz setting for general function Psi as well as in the weighted L-p setting.