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Norms supporting the Lebesgue differentiation theorem
- Publication Year :
- 2018
-
Abstract
- A version of the Lebesgue differentiation theorem is offered, where the [Formula: see text] norm is replaced with any rearrangement-invariant norm. Necessary and sufficient conditions for a norm of this kind to support the Lebesgue differentiation theorem are established. In particular, Lorentz, Orlicz and other customary norms for which Lebesgue’s theorem holds are characterized.
- Subjects :
- Pure mathematics
Mathematics::Dynamical Systems
General Mathematics
Lorentz transformation
Lebesgue differentiation theorem
Mathematics::Classical Analysis and ODEs
010103 numerical & computational mathematics
Orlicz spaces
Lebesgue integration
01 natural sciences
rearrangement-invariant spaces
Lebesgue points, Rearrangement-invariant norms, Maximal operators, Orlicz spaces, Lorentz spaces
symbols.namesake
Lebesgue differentiation theorem, rearrangement-invariant spaces, Lorentz spaces, Orlicz spaces, Marcinkiewicz spaces
FOS: Mathematics
0101 mathematics
Mathematics
Mathematics::Functional Analysis
Marcinkiewicz spaces
Applied Mathematics
46E35, 46E30
010102 general mathematics
Functional Analysis (math.FA)
Mathematics - Functional Analysis
Lorentz spaces
Norm (mathematics)
symbols
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....e4fb20b3e23b4efa7e2b8b51fc0c3fda