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Convolution structures for an Orlicz space with respect to vector measures on a compact group
Published online by Cambridge University Press: 26 March 2021
Abstract
The aim of this paper is to present some results about the space $L^{\varPhi }(\nu ),$ where $\nu$
is a vector measure on a compact (not necessarily abelian) group and $\varPhi$
is a Young function. We show that under natural conditions, the space $L^{\varPhi }(\nu )$
becomes an $L^{1}(G)$
-module with respect to the usual convolution of functions. We also define one more convolution structure on $L^{\varPhi }(\nu ).$
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 1 , February 2021 , pp. 87 - 98
- Copyright
- Copyright © The Author(s) 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society
References
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