Reverse Hölder inequalities revisited : Interpolation, Extrapolation, Indices and Doubling

• Autores: Corvalán, Álvaro; Milman, Mario
• Año de publicación: 2021
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Pure and Applied Functional Analysis. 2021; 6(3): 565-604
• Materia: Functional Analysis; Reverse Hölder; Weights; Interpolation; Extrapolation; Self-Improvement; Indices; Matemáticas
• Institución: Universidad Nacional de General Sarmiento

Revista con referato
Fil: Corvalán, Álvaro. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina.
Extending results in [50] and [49] we characterize the classical classes of weights that satisfy reverse Hölder inequalities in terms of indices of suitable families of K?functionals of the weights. In particular, we introduce a Samko type of index (cf. [41]) for families of functions, that is based on quasi-monotonicity, and use it to provide an index characterization of the RHp classes, as well as the limiting class RH = RHLLogL =. S p>1 RHp (cf. [8]), which in the abstract case involves extrapolation spaces. Reverse Hölder inequalities associated to L(p, q) norms, and non-doubling measures are also treated.