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Function Spaces with Bounded L p Means and Their Continuous Functionals
Author
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-26, 26 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-02-18
Country of Publication
Egypt
No. of Pages
26
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Picardello, Massimo A.. 2014. Function Spaces with Bounded L p Means and Their Continuous Functionals. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-26.
https://search.emarefa.net/detail/BIM-1014328
Modern Language Association (MLA)
Picardello, Massimo A.. Function Spaces with Bounded L p Means and Their Continuous Functionals. Abstract and Applied Analysis No. 2014 (2014), pp.1-26.
https://search.emarefa.net/detail/BIM-1014328
American Medical Association (AMA)
Picardello, Massimo A.. Function Spaces with Bounded L p Means and Their Continuous Functionals. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-26.
https://search.emarefa.net/detail/BIM-1014328
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1014328