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Proceedings of the American Mathematical Society

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

 

 

Maximal operators and capacity


Author: David R. Adams
Journal: Proc. Amer. Math. Soc. 34 (1972), 152-156
MSC: Primary 42A92; Secondary 31B15
DOI: https://doi.org/10.1090/S0002-9939-1972-0350314-1
MathSciNet review: 0350314
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Abstract: It is shown that many maximal functions defined on the $ {L_p}$ spaces are bounded operators on $ {L_p}$ if and only if they satisfy a capacitary weak type inequality.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0350314-1
Keywords: Capacity, maximal functions, Fourier series, singular integrals, $ {L_p}$ spaces
Article copyright: © Copyright 1972 American Mathematical Society