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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Generalized Hankel conjugate transformations on rearrangement invariant spaces

Author: R. A. Kerman
Journal: Trans. Amer. Math. Soc. 232 (1977), 111-130
MSC: Primary 42A40; Secondary 44A25
MathSciNet review: 0450882
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Abstract: The boundedness properties of the generalized Hankel conjugate transformations $ {H_\lambda }$ on certain weighted Lebesgue spaces are studied. These are used to establish a boundedness criterion for the $ {H_\lambda }$ on the more general class of rearrangement invariant spaces. The positive operators in terms of which the criterion is given are used to construct pairs of spaces between which the $ {H_\lambda }$ are continuous; in particular, a natural analogue of a well-known result of Zygmund concerning the classical conjugate function operator is obtained for the $ {H_\lambda }$.

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Keywords: Hankel conjugate transformation, boundedness, rearrangement invariant space, Lebesgue space, Lorentz space, Orlicz space
Article copyright: © Copyright 1977 American Mathematical Society

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