Analysis Related to All Admissible Type Parameters in the Jacobi Setting

作者：Nowak Adam^*; Sjogren Peter; Szarek Tomasz Z

来源：Constructive Approximation, 2015, 41(2): 185-218.

DOI：10.1007/s00365-015-9275-5

• Jacobi expansion
• Jacobi-Poisson kernel
• Maximal operator
• Riesz transform
• Square function
• Spectral Multiplier
• Calderon-Zygmund operator

We derive an integral representation for the Jacobi-Poisson kernel valid for all admissible type parameters in the context of Jacobi expansions. This enables us to develop a technique for proving standard estimates in the Jacobi setting that works for all possible and . As a consequence, we can prove that several fundamental operators in the harmonic analysis of Jacobi expansions are (vector-valued) Caldern-Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory. The new Jacobi-Poisson kernel representation also leads to sharp estimates of this kernel. The paper generalizes methods and results existing in the literature but valid or justified only for a restricted range of alpha and beta.

• 出版日期2015-4