Sharp Marchaud and converse inequalities in Orlicz spaces

Authors:
Z. Ditzian and A. V. Prymak

Journal:
Proc. Amer. Math. Soc. **135** (2007), 1115-1121

MSC (2000):
Primary 26A15, 26B99, 41A27; Secondary 41A63, 46E30

Published electronically:
October 27, 2006

MathSciNet review:
2262913

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For spaces on , and , sharp versions of the classical Marchaud inequality are known. These results are extended here to Orlicz spaces (on , and ) for which is convex for some , , where is the Orlicz function. Sharp converse inequalities for such spaces are deduced.

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Additional Information

**Z. Ditzian**

Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Email:
zditzian@math.ualberta.ca

**A. V. Prymak**

Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Email:
prymak@gmail.com

DOI:
https://doi.org/10.1090/S0002-9939-06-08682-5

Keywords:
Sharp Marchaud inequality,
Orlicz spaces,
power-type $q$.

Received by editor(s):
November 9, 2005

Published electronically:
October 27, 2006

Additional Notes:
The first author was supported by NSERC grant of Canada A4816.

This research was done while the second author visited University of Alberta in 2005; the visit was supported by the first author’s NSERC grant of Canada A4816

Communicated by:
Jonathan M. Borwein

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.