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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Endpoint estimates for the maximal operator associated to spherical partial sums on radial functions


Authors: Elena Romera and Fernando Soria
Journal: Proc. Amer. Math. Soc. 111 (1991), 1015-1022
MSC: Primary 42B25
MathSciNet review: 1068130
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Abstract: Let $ Tf(x) = {\sup _{R > 0}}\left\vert {{S_R}f(x)} \right\vert$ where $ {S_R}$ is the spherical partial sum operator. We show that $ T$ is bounded from the Lorentz space $ {L_{{p_i},1}}({{\mathbf{R}}^n})$ into $ {L_{{p_i},\infty }}({{\mathbf{R}}^n}),i = 0,1$ when acting on radial functions and where $ {p_0} = \tfrac{{2n}}{{n + 1}},{p_1} = \tfrac{{2n}}{{n - 1}}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1068130-6
PII: S 0002-9939(1991)1068130-6
Article copyright: © Copyright 1991 American Mathematical Society