Estimates of difference norms for functions in anisotropic Sobolev spaces

  1. Kolyada, V.I. 2
  2. Pérez, F.J. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Karlstad University
    info

    Karlstad University

    Karlstad, Suecia

    ROR https://ror.org/05s754026

Revista:
Mathematische Nachrichten

ISSN: 0025-584X

Año de publicación: 2004

Volumen: 267

Número: 267

Páginas: 46-64

Tipo: Artículo

DOI: 10.1002/MANA.200310152 SCOPUS: 2-s2.0-4644234932 WoS: WOS:000221330900004 GOOGLE SCHOLAR

Otras publicaciones en: Mathematische Nachrichten

Repositorio institucional: lock_openAcceso abierto Editor

Resumen

We investigate the spaces of functions on ℝ n for which the generalized partial derivatives D k rk f exist and belong to different Lorentz spaces L pk, sk. For the functions in these spaces, the sharp estimates of the Besov type norms are found. The methods used in the paper are based on estimates of non-increasing rearrangements. These methods enable us to cover also the case when some of the p k's are equal to 1. © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.