CRITERION FOR THE COINCIDENCE OF STRONG AND WEAK ORLICZ SPACES

Maria Rosaria Formica, Eugeny Ostrovsky

Research output: Contribution to journalArticlepeer-review

Abstract

We provide necessary and sufficient conditions for the coincidence, up to equivalence of the norms, between strong and weak Orlicz spaces. Roughly speaking, this coincidence holds true only for the so-called exponential spaces. We also find the exact value of the embedding constant which appears in the corresponding norm inequality.

Original languageEnglish
Pages (from-to)381-397
Number of pages17
JournalStudia Scientiarum Mathematicarum Hungarica
Volume58
Issue number3
DOIs
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2021 Akadémiai Kiadó, Budapest.

Funding

ACKNOWLEDGEMENT. The first author has been partially supported by the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and by Università degli Studi di Napoli Parthenope through the project “sostegno alla Ricerca individuale”. The first author has been partially supported by the Gruppo Nazionale per l'Analisi Matematica, la Probabilit? e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and by Universit? degli Studi di Napoli Parthenope through the project ?sostegno alla Ricerca individuale?. The second author is grateful to M. Sgibnev (Novosibirsk, Russia) for sending his interesting articles.

FundersFunder number
GNAMPA
Gruppo Nazionale per l'Analisi Matematica, la Probabilit?
Studi di Napoli Parthenope
Universit?
Istituto Nazionale di Alta Matematica "Francesco Severi"
Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
Università degli Studi di Napoli Parthenope

    Keywords

    • Markov-Tchebychev's inequality
    • expectation
    • measure
    • strong and weak Orlicz spaces
    • tail function and tail norm

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