A version of the Lebesgue differentiation theorem is offered, where the L^p 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.
Norms supporting the Lebesgue differentiation theorem / Cavaliere, Paola; Cianchi, Andrea; Pick, Lubos; Slavikova, Lenka. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - STAMPA. - 20:(2018), pp. 1-33. [10.1142/S0219199717500201]
Norms supporting the Lebesgue differentiation theorem
CIANCHI, ANDREA;
2018
Abstract
A version of the Lebesgue differentiation theorem is offered, where the L^p 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.
| File | Dimensione | Formato | |
|---|---|---|---|
|
1512.03202.pdf
Open Access dal 02/02/2019
Tipologia:
Versione finale referata (Postprint, Accepted manuscript)
Licenza:
Open Access
Dimensione
275.18 kB
Formato
Adobe PDF
|
275.18 kB | Adobe PDF |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
