Generalized Hankel conjugate transformations on rearrangement invariant spaces

R. A. Kerman
1977 Transactions of the American Mathematical Society  
The boundedness properties of the generalized Hankel conjugate transformations Hx on certain weighted Lebesgue spaces are studied. These are used to establish a boundedness criterion for the Hx 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 Hx are continuous; in particular, a natural analogue of a wellknown result of Zygmund concerning the classical conjugate
more » ... sical conjugate function operator is obtained for the Hx.
doi:10.1090/s0002-9947-1977-0450882-4 fatcat:sezlik7emnfrdmutxa2lnu4mom