论文信息 - An endpoint estimate for the Kunze-Stein phenomenon and related maximal operators

An endpoint estimate for the Kunze-Stein phenomenon and related maximal operators

One of the purposes of this paper is to prove that if G is a noncompact connected semisimple Lie group of real rank one with flnite center, then L 2;1 (G)⁄L 2;1 (G)µ L 2;1 (G): Let K be a maximal compact subgroup of G and X = G=K a symmetric space of real rank one. We will also prove that the noncentered maximal operator M2f(z) = sup2B 1 jBj Z B jf(z 0 )jdz 0 is bounded from L 2;1 (X )t oL 2;1 (X) and from L p (X )t oL p (X) in the sharp range of exponents p2 (2;1]. The supremum in the deflnition ofM2f(z )i s taken over all balls containing the point z.

A. Ionescu

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