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Indices of O-regular variation for weight functions and weight sequences

Abstract: A plethora of spaces in Functional Analysis (Braun?Meise?Taylor and Carleman ultradifferentiable and ultraholomorphic classes; Orlicz, Besov, Lipschitz, Lebesque spaces, to cite the main ones) are defined by means of a weighted structure, obtained from a weight function or sequence subject to standard conditions entailing desirable properties (algebraic closure, stability under operators, interpolation, etc.) for the corresponding spaces. The aim of this paper is to stress or reveal the true nature of these diverse conditions imposed on weights, appearing in a scattered and disconnected way in the literature: they turn out to fall into the framework of O-regular variation, and many of them are equivalent formulations of one and the same feature. Moreover, we study several indices of regularity/growth for both functions and sequences, which allow for the rephrasing of qualitative properties in terms of quantitative statements.

 Fuente: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas volume 113 (2019), pages3659-3697

Editorial: Springer

 Fecha de publicación: 27/07/2019

Nº de páginas: 39

Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s13398-019-00724-2

ISSN: 1578-7303,1579-1505

Proyecto español: MTM2016-77642-C2-1-P

Url de la publicación: https://doi.org/10.1007/s13398-019-00724-2