Besov spaces with positive smoothness on image, embeddings and growth envelopes Original Research Article

We characterise Besov spaces with positive smoothness on RnRn, obtained by different approaches. First we present two settings View the MathML sourceBp,qs(Rn), View the MathML sourceBp,qs(Rn) associated to definitions by differences and Fourier-analytical methods and give an equivalent characterisation in terms of subatomic decompositions for the spaces View the MathML sourceBp,qs. We study their connections and diversity, as well as embeddings between Besov spaces and into Lorentz spaces. Secondly, we determine their growth envelopes View the MathML sourceEG(Bp,qs(Rn)) for 00s>0, and finally discuss some applications