Function spaces of Nikolskii type on compact manifold

Bondioli, Cristiana. "Function spaces of Nikolskii type on compact manifold." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 3.3 (1992): 185-194. <http://eudml.org/doc/244171>.

@article{Bondioli1992,
abstract = {Nikolskii spaces were defined by way of translations on \( \mathbb\{R\}^\{n\} \) and by way of coordinate maps on a differentiable manifold. In this paper we prove that, for functions with compact support in \( \mathbb\{R\}^\{n\} \), we get an equivalent definition if we replace translations by all isometries of \( \mathbb\{R\}^\{n\} \). This result seems to justify a definition of Nikolskii type function spaces on riemannian manifolds by means of a transitive group of isometries (provided that one exists). By approximation theorems, we prove that - for homogeneous spaces of compact connected Lie groups - our definition is equivalent to the classical one.},
author = {Bondioli, Cristiana},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Nikolskii spaces; Isometry groups; Compact homogeneous spaces; Nikolskii space; space of absolutely integrable functions; differentiable manifold; Riemannian manifold; transitive group of isometries; homogeneous spaces of compact connected Lie groups},
language = {eng},
month = {9},
number = {3},
pages = {185-194},
publisher = {Accademia Nazionale dei Lincei},
title = {Function spaces of Nikolskii type on compact manifold},
url = {http://eudml.org/doc/244171},
volume = {3},
year = {1992},
}

TY - JOUR
AU - Bondioli, Cristiana
TI - Function spaces of Nikolskii type on compact manifold
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1992/9//
PB - Accademia Nazionale dei Lincei
VL - 3
IS - 3
SP - 185
EP - 194
AB - Nikolskii spaces were defined by way of translations on \( \mathbb{R}^{n} \) and by way of coordinate maps on a differentiable manifold. In this paper we prove that, for functions with compact support in \( \mathbb{R}^{n} \), we get an equivalent definition if we replace translations by all isometries of \( \mathbb{R}^{n} \). This result seems to justify a definition of Nikolskii type function spaces on riemannian manifolds by means of a transitive group of isometries (provided that one exists). By approximation theorems, we prove that - for homogeneous spaces of compact connected Lie groups - our definition is equivalent to the classical one.
LA - eng
KW - Nikolskii spaces; Isometry groups; Compact homogeneous spaces; Nikolskii space; space of absolutely integrable functions; differentiable manifold; Riemannian manifold; transitive group of isometries; homogeneous spaces of compact connected Lie groups
UR - http://eudml.org/doc/244171
ER -