Fernández Besoy, BlancaCobos Díaz, FernandoTriebel, Hans2023-06-172023-06-1720210025-583110.1007/s00208-021-02168-9https://hdl.handle.net/20.500.14352/7997We work with Triebel–Lizorkin spaces FsqLp,r(Rn) and Besov spaces BsqLp,r(Rn) with Lorentz smoothness. Using their characterizations by real interpolation we show how to transfer a number of properties of the usual Triebel–Lizorkin and Besov spaces to the spaces with Lorentz smoothness. In particular, we give results on diffeomorphisms, extension operators, multipliers and we also show sufficient conditions on parameters for FsqLp,r(Rn) and BsqLp,r(Rn) to be multiplication algebras.engjournal articlehttps://doi.org/10.1007/s00208-021-02168-9https://link.springer.com/article/10.1007/s00208-021-02168-9open access517.98517.982.2Triebel-Lizorkin-Lorentz spacesBesov-Lorentz spacesReal interpolationMultiplicationsAnálisis funcional y teoría de operadores