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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Convolution operators of weak type $ (p,\,p)$ which are not of strong type $ (p,\,p)$


Author: Ryszard Szwarc
Journal: Proc. Amer. Math. Soc. 89 (1983), 184-185
MSC: Primary 43A15; Secondary 22D99, 43A22
DOI: https://doi.org/10.1090/S0002-9939-1983-0706538-1
MathSciNet review: 706538
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Abstract: We give an example of a locally compact group $ G$ for which, for every $ p$ with $ 2 < p < \infty $, there exists an operator of weak type $ (p,p)$ commuting with the right translations on $ G$ which is not of strong type $ (p,p)$. This gives a negative solution of E. M. Stein's problem.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0706538-1
Keywords: Free group, convolution operator, strong type, weak type
Article copyright: © Copyright 1983 American Mathematical Society