Lebesgue's Differentiation Theorems in R.I. Quasi-Banach Spaces and Lorentz Spaces Γp,w
Joint Authors
Kaminska, Anna
Ciesielski, Maciej
Source
Journal of Function Spaces and Applications
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-28, 28 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-03-20
Country of Publication
Egypt
No. of Pages
28
Main Subjects
Abstract EN
The paper is devoted to investigation of new Lebesgue's type differentiation theorems (LDT) in rearrangement invariant (r.i.) quasi-Banach spaces E and in particular on Lorentz spaces Γp,w={f:∫(f**)pw<∞} for any 0
The first type of LDT in the spirit of Stein (1970), characterizes the convergence of quasinorm averages of f∈E, where E is an order continuous r.i.
quasi-Banach space.
The second type of LDT establishes conditions for pointwise convergence of the best or extended best constant approximants fϵ of f∈Γp,w or f∈Γp-1,w, 1
In the last section it is shown that the extended best constant approximant operator assumes a unique constant value for any function f∈Γp-1,w, 1
American Psychological Association (APA)
Ciesielski, Maciej& Kaminska, Anna. 2012. Lebesgue's Differentiation Theorems in R.I. Quasi-Banach Spaces and Lorentz Spaces Γp,w. Journal of Function Spaces and Applications،Vol. 2012, no. 2012, pp.1-28.
https://search.emarefa.net/detail/BIM-490209
Modern Language Association (MLA)
Ciesielski, Maciej& Kaminska, Anna. Lebesgue's Differentiation Theorems in R.I. Quasi-Banach Spaces and Lorentz Spaces Γp,w. Journal of Function Spaces and Applications No. 2012 (2012), pp.1-28.
https://search.emarefa.net/detail/BIM-490209
American Medical Association (AMA)
Ciesielski, Maciej& Kaminska, Anna. Lebesgue's Differentiation Theorems in R.I. Quasi-Banach Spaces and Lorentz Spaces Γp,w. Journal of Function Spaces and Applications. 2012. Vol. 2012, no. 2012, pp.1-28.
https://search.emarefa.net/detail/BIM-490209
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-490209