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Applications of an Inverse Abel Transform for Jacobi Analysis: Weak-$L^1$ Estimates and the Kunze-Stein Phenomenon
For the Jacobi hypergroup $({\bf R}_+,\Delta,*)$, the weak-$L^1$ estimate of the Hardy-Littlewood maximal operator was obtained by W. Bloom and Z. Xu, later by J. Liu, and the endpoint estimate for the Kunze-Stein phenomenon was obtained by J. Liu. In this paper we shall give alternative proofs based on the …