On one extension theorem dealing with weighted Orlicz-Slobodetskii space. Analysis on cube

Abstract

Abstract. Having given weightρ = ρ (dist(x,∂ Q)) defined on cube Q and Orlicz function R , we construct the weight ω ρ (·,·) defined on ∂ Q×∂ Q and extension operator Ext

Well posedness and regularity for heat equation with the initial condition in weighted Orlicz–Slobodetskii space subordinated to Orlicz space like $$\lambda (\mathrm{log} \lambda )^\alpha $$ λ ( log λ ) α and the logarithmic weight

“…where Y R,R ω (Q ) is weighted Orlicz-Slobodetskii space introduced in [11,12]. In particular more precise statement than that in Corollary 5.1 holds.…”

“…Recently first author and Dhara [11,12] were investigating properties of the extension operator from Orlicz-Slobodetski type space to Orlicz-Sobolev space in the weighted setting. See also [7,8,29,32,38], for some interesting related results.…”

Traces of weighted function spaces: Dyadic norms and Whitney extensions

“…Here we present a direct proof of the equivalence of the (quasi-)norm (8) with the standard Besov quasi-norm (10). Proposition 7.1.…”

On equivalent conditions for the validity of Poincaré inequality on weighted Sobolev space with applications to the solvability of degenerated PDEs involving p-Laplacian

“…For results dealing with power weights we refer e.g. to [26,33,40,44,45], while for results in the general setting we refer to our recent results [13,14].…”