Generalized Hankel conjugate transformations on rearrangement invariant spaces

Kerman, R. A.

doi:10.1090/S0002-9947-1977-0450882-4

Generalized Hankel conjugate transformations on rearrangement invariant spaces
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by R. A. Kerman PDF

Trans. Amer. Math. Soc. 232 (1977), 111-130 Request permission

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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