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Mellin multipliers and radially symmetric Riesz potentials

Published online by Cambridge University Press:  20 January 2009

W. Lamb  and
S. E. Schiavone
W. Lamb
Affiliation:
Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, Scotland
S. E. Schiavone
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
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Abstract

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Riesz potentials with radially symmetric densities are examined from the standpoint of Mellin multipliers. Various results are deduced from the underlying multipliers, including a decomposition of the potential into a product of Erdélyi-Kober fractional integrals. Distributional versions of these results are also produced and shown to be valid under less severe restrictions on the parameters than those required in a weighted Lp setting.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 3 , October 1994 , pp. 493 - 507
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

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