We study the existence of an extension operator Lambda: W1,phi(S2) -> W1,psi(Rn). We assume that cp is an element of Phi w(S2) has generalized Orlicz growth, 0 is an element of Phi w(Rn) is an extension of cp, and that S2 subset of Rn is an (e, 5)-domain. Special cases include the classical constant exponent case, the Orlicz case, the variable exponent case, and the double phase case.

(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).