Generalized Hankel Conjugate Transformations on Rearrangement Invariant Spaces
Copyright policy )Generalized Hankel Conjugate Transformations on Rearrangement Invariant Spaces
The boundedness properties of the generalized Hankel conjugate transformations H λ {H_\lambda } on certain weighted Lebesgue spaces are studied. These are used to establish a boundedness criterion for the H λ {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 λ {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 λ {H_\lambda } .
Special integral transforms (Legendre, Hilbert, etc.), Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Special integral transforms (Legendre, Hilbert, etc.), Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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