Function spaces of Lorentz-Sobolev type: Atomic decompositions, characterizations in terms of wavelets, interpolation and multiplications

摘要

We establish atomic decompositions and characterizations in terms of wavelets for Besov-Lorentz spaces (BqLp,r)-L-s(R-n) and for Triebel-Lizorkin-Lorentz spaces (FqLp,r)-L-s(R-n) in the whole range of parameters. As application we obtain new interpolation formulae between spaces of Lorentz-Sobolev type. We also remove the restrictions on the parameters in a result of Peetre on optimal embeddings of Besov spaces. Moreover, we derive results on diffeomorphisms, extension operators and multipliers for (BqLp,infinity)-L-s(R-n). Finally, we describe (BqLp,r)-L-s(R-n) as an approximation space, which allows us to show new sufficient conditions on parameters for (BqLp,r)-L-s(R-n) to be a multiplication algebra. (C) 2022 The Authors. Published by Elsevier Inc.