2015/01/11 by António Caetano, Caetano, António, Dorothee Haroske +1 · 1 citation
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46E35 #Secondary 28A80 #math.FA #msc:28A80 #msc:46E35
paper · pdf · doi:10.48550/arxiv.1501.02796
arXiv admin note: text overlap with arXiv:1501.02493
arxiv created 2015/11/01 · arxiv updated 2015/11/03
Let Γ be a fractal h-set and \mathbbBσp,q(Γ) be a trace space of Besov type defined on Γ. While we dealt in [9] with growth envelopes of such spaces mainly and investigated the existence of traces in detail in [12], we now study continuous embeddings between different spaces of that type on Γ. We obtain necessary and sufficient conditions for such an embedding to hold, and can prove in some cases complete characterisations. It also includes the situation when the target space is of type Lr(Γ) and, as a by-product, under mild assumptions on the h-set Γ we obtain the exact conditions on σ, p and q for which the trace space \mathbbBσp,q(Γ) exists. We can also refine some embedding results for spaces of generalised smoothness on \mathbb Rn.