Paley type inequalities for orthogonal series with vector-valued coefficients
- Garcia-Cuerva, J. 1
- Kazarian, K.S. 1
- Kolyada, V.I. 2
-
1
Universidad Autónoma de Madrid
info
-
2
Universidad de La Rioja
info
ISSN: 0236-5294
Argitalpen urtea: 2001
Alea: 89
Zenbakia: 1-2
Orrialdeak: 151-183
Mota: Artikulua
Beste argitalpen batzuk: Acta Mathematica Hungarica
Laburpena
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.