RT Journal Article
T1 Function spaces of Lorentz-Sobolev type: Atomic decompositions, characterizations in terms of wavelets, interpolation and multiplications
A1 Fernández Besoy, Blanca
A1 Cobos Díaz, Fernando
AB 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.
PB Elsevier
SN 0022-1236
YR 2022
FD 2022-03-04
LK https://hdl.handle.net/20.500.14352/71358
UL https://hdl.handle.net/20.500.14352/71358
LA eng
NO CRUE-CSIC (Acuerdos Transformativos 2022)
NO Ministerio de Ciencia, Innovación y Universidades (España)/Fondo Europeo de Desarrollo Regional
NO Ministerio de Educación, Formación Profesional y Deportes (España)
DS Docta Complutense
RD 10 abr 2025