Applications of an inverse abel transform for jacobi analysis: Weak-l1 estimates and the kunze-Stein phenomenon

Takeshi Kawazoe

研究成果: Article

1 引用 (Scopus)

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For the Jacobi hypergroup (R+,Δ,), the weak-L1 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 inverse Abel transform for the Jacobi hypergroup. The point is that the Abel transform reduces the convolution to the Euclidean convolution. More generally, let T be the Hardy-Littlewood maximal operator, the Poisson maximal operator or the Littlewood- Paley g-function for the Jacobi hypergroup, which are defined by using. Then we shall give a standard shape of Tf for f ∈ L1(Δ), from which its weak-L1 estimate follows. Concerning the endpoint estimate of the Kunze-Stein phenomenon, though Liu used the explicit form of the kernel of the convolution, we shall give a proof without using the kernel form.

元の言語English
ページ(範囲)77-112
ページ数36
ジャーナルTokyo Journal of Mathematics
41
発行部数1
DOI
出版物ステータスPublished - 2018 6

ASJC Scopus subject areas

  • Mathematics(all)

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