On inequalities for integral operators
1970 ◽
Vol 11
(2)
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pp. 126-133
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Keyword(s):
In two papers [3] and [4], the author has extended the inequality of Schur (Theorem 319 of [2]) to cases involving kernels which satisfy identities of the formThe purpose of this paper is to prove a general inequality, which includes the above and also the inequality of Young (Theorem 281 of [2]) as special cases. We shall give the results a general setting by considering functions defined on abstract measure spaces. From this we shall deduce an extension to n dimensions of the results given in [3], which also generalises a similar extension of the Schur inequality given by Stein and Weiss. In fact some cases of the other results given in [5] will follow directly from our theorem.
1975 ◽
Vol 78
(3)
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pp. 461-469
Keyword(s):
1906 ◽
Vol 41
(3)
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pp. 651-676
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Keyword(s):
2012 ◽
Vol 142
(5)
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pp. 1003-1025
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2010 ◽
Vol 140
(1)
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pp. 31-48
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1981 ◽
Vol 88
(3-4)
◽
pp. 203-217
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Keyword(s):
Keyword(s):
1904 ◽
Vol 24
◽
pp. 233-239
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