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Convolution structures for an Orlicz space with respect to vector measures on a compact group

Part of:Abstract harmonic analysisMeasures, integration, derivative, holomorphy

Published online by Cambridge University Press:  26 March 2021

Manoj Kumar and
N. Shravan Kumar
Manoj Kumar
Affiliation:
Department of Mathematics, Indian Institute of Technology Delhi, New Delhi 110016, India (manojk9t3@gmail.com; shravankumar@maths.iitd.ac.in)
N. Shravan Kumar
Affiliation:
Department of Mathematics, Indian Institute of Technology Delhi, New Delhi 110016, India (manojk9t3@gmail.com; shravankumar@maths.iitd.ac.in)
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Abstract

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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 $L^{\varPhi }(\nu ).$

Keywords

Compact groupOrlicz spacevector measureconvolution

MSC classification

Primary:43A77: Analysis on general compact groups43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.
Secondary:46G10: Vector-valued measures and integration

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 1 , February 2021, pp. 87 - 98
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Copyright
Copyright © The Author(s) 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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