2026-06-02T18:39:49Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/713582024-07-17T13:06:51Zcom_20.500.14352_14col_20.500.14352_15

Function spaces of Lorentz-Sobolev type: Atomic decompositions, characterizations in terms of wavelets, interpolation and multiplications Fernández Besoy, Blanca Cobos Díaz, Fernando 517.98 Besov-Lorentz spaces Triebel-Lizorkin-Lorentz spaces Approximation spaces Multiplication algebras Análisis funcional y teoría de operadores CRUE-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. Ministerio de Ciencia, Innovación y Universidades (España)/Fondo Europeo de Desarrollo Regional Ministerio de Educación, Formación Profesional y Deportes (España) Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-22T10:41:04Z 2023-06-22T10:41:04Z 2022-03-04 journal article https://hdl.handle.net/20.500.14352/71358 0022-1236 10.1016/j.jfa.2022.109452 eng MTM2017-84058-P FPU16/02420 Atribución-NoComercial-SinDerivadas 3.0 España https://creativecommons.org/licenses/by-nc-nd/3.0/es/ open access application/pdf application/pdf Elsevier