On trace spaces of 2-microlocal type spaces

We study traces in 2-microlocal Triebel–Lizorkin spaces with variable integrability Fp(⋅),q(⋅)w(Rn) on hyperplanes using atomic decompositions. Our results cover spaces of variable smoothness and variable integrability and also weighted spaces studied extensively in recent years. We also study the trace of Besov spaces Bp(⋅),qw(Rn) and Triebel–Lizorkin spaces Fp(⋅),q(⋅)w(Rn) in a limiting situation, i.e.  , when wj(x)=2j1p(x) for all x∈Rnx∈Rn and j∈N0j∈N0.