This paper studies typical Banach and complete seminormed spaces of locally summable functions and their continuous functionals. Such spaces were introduced long ago as a natural environment to study almost periodic functions (Besicovitch, 1932; Bohr and Fölner, 1944) and are defined by boundedness of suitable L p means. The supremum of such means defines a norm (or a seminorm, in the case of the full Marcinkiewicz space) that makes the respective spaces complete. Part of this paper is a review of the topological vector space structure, inclusion relations, and convolution operators. Then we expand and improve the deep theory due to Lau of representation of continuous functional and extreme points of the unit balls, adapt these results to Stepanoff spaces, and present interesting examples of discontinuous functionals that depend only on asymptotic values.

Picardello, A.m. (2014). Function Spaces with Bounded L-p Means and Their Continuous Functionals. ABSTRACT AND APPLIED ANALYSIS, 2014, 1-26 [10.1155/2014/609525].

Function Spaces with Bounded L-p Means and Their Continuous Functionals

PICARDELLO, ANGELO MASSIMO
2014

Abstract

This paper studies typical Banach and complete seminormed spaces of locally summable functions and their continuous functionals. Such spaces were introduced long ago as a natural environment to study almost periodic functions (Besicovitch, 1932; Bohr and Fölner, 1944) and are defined by boundedness of suitable L p means. The supremum of such means defines a norm (or a seminorm, in the case of the full Marcinkiewicz space) that makes the respective spaces complete. Part of this paper is a review of the topological vector space structure, inclusion relations, and convolution operators. Then we expand and improve the deep theory due to Lau of representation of continuous functional and extreme points of the unit balls, adapt these results to Stepanoff spaces, and present interesting examples of discontinuous functionals that depend only on asymptotic values.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - Analisi Matematica
eng
Con Impact Factor ISI
Picardello, A.m. (2014). Function Spaces with Bounded L-p Means and Their Continuous Functionals. ABSTRACT AND APPLIED ANALYSIS, 2014, 1-26 [10.1155/2014/609525].
Picardello, Am
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/89973
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