Fourier-Jacobi展开的Riesz平均

Riesz Means of Fourier-Jacobi Expansion

对ｆ∈Ｌｐ（Ｒ＋，Δ（ｔ）ｄｔ），Δ（ｔ）＝（２ｓｉｎｈｔ）２α＋１（２ｃｏｓｈｔ）２β＋１，１ｐ２，本文证明了当Ｒｅｚ＞（２／ｐ－１）（α＋１／２）时，ｆ的Ｆｏｕｒｉｅｒ－Ｊａｃｏｂｉ展开的ｚ－阶Ｒｉｅｓｚ平均几乎处处收敛于ｆ．

In this paper, we prove that if f∈L p( R +, Δ (t)dt),  Δ (t)=(2 sinh t) 2α+1 ·(2 cosh t) 2β+1 ,1p2, the Riesz means of order z of f with respect to Fourier-Jacobi expansion is convergent almost everywhere for Re z>(2/p-1)(α+1/2). This generalizes the earlier results of Giulini S. and Mauceri G. on noncompact symmetric space of real rank one.