We define Hilbert transform and conjugate Poisson integrals associated with the Jacobi differential operator on (0, +∞). We prove that these operators are bounded in the appropriate Lebesgue spaces L p , 1 < p < +∞. In this study, the tools used are the Littlewood–Paley g-functions associated with the Poisson semigroup and the supplementary Poisson semigroup which we introduce in this paper.
Positivity – Springer Journals
Published: May 7, 2010
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