On the comparison of the Marcinkiewicz and Luxemburg norms of the exponential space

On the comparison of the Marcinkiewicz and Luxemburg norms of the exponential space

The exponential space, which is a Banach function space, can be defined with two very differently looking, but equivalent norms. In this paper, we give estimates for the best constants of the ratio of these two norms. Our result answers a question of C. Bennett, and R. Sharpley.

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Veröffentlicht in:Mathematical notes (Miskolci Egyetem (Hungary)) 2023, Vol.24 (2), p.909-914
1. Verfasser: Mezo, István
Format: Artikel
Sprache:eng
Schlagworte:
Function space
Norms
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Zusammenfassung:The exponential space, which is a Banach function space, can be defined with two very differently looking, but equivalent norms. In this paper, we give estimates for the best constants of the ratio of these two norms. Our result answers a question of C. Bennett, and R. Sharpley.
ISSN:1787-2405
1787-2413
DOI:10.18514/MMN.2023.4045