We obtain a quantitative weighted bound for the Calderón commutator $\mathcal C_\Omega $ which is typical example of non-convolution Calderón–Zygmund operator under condition $\Omega \in L^\infty (\mathbb S^{n-1})$; this best known quantita

It is shown that if the Boyd indices of the rearrangement invariant Banach function space Lρ(R) are strictly between 0 and 1, ρ is an absolutely continuous function norm, Ω is a domain from R satisfying the restricted cone condition, denoting by ω the restriction of ρ to Ω, there exists an extension operator for the abstract Sobolev space W Lω(Ω). This is a generalization to abstract Sobolev sp...