ON ONE EXTENSION THEOREM DEALING WITH WEIGHTED ORLICZ-SLOBODETSKII SPACE. ANALYSIS ON CUBE

Having given weight (rho) over tilde = rho (dist(x, partial derivative Q)) defined on cube Q and Orlicz function R, we construct the weight omega(rho) (., .) defined on partial derivative Q x partial derivative Q and extension operator Ext(L) : Lip(d) (partial derivative Q) bar right arrow Lip(Q) from Lipschitz functions defined on partial derivative Q with certain restricted support to Lipschitz functions defined on Q, independent of. and R, in such away that ExtL extends to the bounded operator from certain subspace of weighted Orlicz-Slobodetskii space Y-omega rho(R,R)(partial derivative Q) subordinated to the weight omega(rho) to Orlicz Sobolev space W-rho(1,R). (Q). Result is new in the unweighted Orlicz setting for general function R as well as in the weighted L-p setting.