Paley type inequalities for orthogonal series with vector-valued coefficients

  1. Garcia-Cuerva, J. 1
  2. Kazarian, K.S. 1
  3. Kolyada, V.I. 2
  1. 1 Universidad Autónoma de Madrid
    info

    Universidad Autónoma de Madrid

    Madrid, España

    ROR https://ror.org/01cby8j38

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revue:
Acta Mathematica Hungarica

ISSN: 0236-5294

Année de publication: 2001

Volumen: 89

Número: 1-2

Pages: 151-183

Type: Article

beta Ver similares en nube de resultados
DOI: 10.1023/A:1006704311908 SCOPUS: 2-s2.0-26444475923 WoS: WOS:000167000300012 GOOGLE SCHOLAR

D'autres publications dans: Acta Mathematica Hungarica

Dépôt institutionnel: lock_openAccès ouvert Editor

Objectifs de Développement Durable

Résumé

We investigate the extension to Banach-space-valued functions of the classical inequalities due to Paley for the Fourier coefficients with respect to a general orthonormal system Φ. This leads us to introduce the notions of Paley Φ-type and Φ-cotype for a Banach space and some related concepts. We study the relations between these notions of type and cotype and those previously defined. We also analyze how the interpolation spaces inherit these characteristics from the original spaces, and use them to obtain sharp coefficient estimates for functions taking values in Lorentz spaces. © 2001 Akadémiai Kiadó.