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Proceedings of the American Mathematical Society

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

 

 

A singular integral inequality on a bounded interval


Authors: J. S. Bradley and W. N. Everitt
Journal: Proc. Amer. Math. Soc. 61 (1976), 29-35
MSC: Primary 34B99; Secondary 26A84
MathSciNet review: 0425249
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Abstract: An inequality of the form (1.1) is established, where $ p,q$ are real-valued functions on an interval $ [a,b)$ of the real line, with $ - \infty < a < b < \infty ,p(x) > 0$ on $ [a,b),{\mu _0}$ is a real number and $ f$ is a complex-valued function in a linear manifold so chosen that all three integrals in (1.1) are absolutely convergent. The problem is singular in that while $ {p^{ - 1}} \in L(a,b)$ we require $ q$ to have a behavior at $ b$ of such a form that $ q \notin L(a,b)$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0425249-X
Article copyright: © Copyright 1976 American Mathematical Society