Fernández Besoy, BlancaCobos Díaz, Fernando2023-06-222023-06-222022-03-040022-123610.1016/j.jfa.2022.109452https://hdl.handle.net/20.500.14352/71358CRUE-CSIC (Acuerdos Transformativos 2022)We establish atomic decompositions and characterizations in terms of wavelets for Besov-Lorentz spaces Bsq Lp,r (Rn) and for Triebel-Lizorkin-Lorentz spaces Fsq Lp,r (Rn) 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 Bsq Lp,∞ (Rn). Finally, we describe Bsq Lp,r (Rn) as an approximation space, which allows us to show new sufficient conditions on parameters for Bsq Lp,r (Rn) to be a multiplication algebra.engAtribución-NoComercial-SinDerivadas 3.0 Españahttps://creativecommons.org/licenses/by-nc-nd/3.0/es/journal articlehttps://doi.org/10.1016/j.jfa.2022.109452https://www.sciencedirect.com/science/article/pii/S0022123622000726https://www.sciencedirect.com/science/article/pii/S0022123622000726open access517.98Besov-Lorentz spacesTriebel-Lizorkin-Lorentz spacesApproximation spacesMultiplication algebrasAnálisis funcional y teoría de operadores