Real hardy space for jacobi analysis and its applications

Takeshi Kawazoe

研究成果: Chapter

抄録

Let Formula Presented the weight function on Formula Presented denote the space of even integrable functions on ℝ with respect to Formula Presented and define the radial maximal operator Formula Presented, as usual. We introduce a real Hardy space H1(Δ) as the set of all even locally integrable functions f on ℝ whose radial maximal function Formula Presented belongs to L1(Δ). We shall obtain a relation between H1(Δ) and H1(ℝ). As an application of H1(Δ), we shall consider (H1(Δ),L1(Δ)) boundedness of integral operators associated to the Poisson kernel for Jacobi analysisj the Poisson maximal operator Formula Presented, the Littlewood-Paley g-function, and the Lusin area function S. They are bounded on Lp(Δ) for p >1, but not true for p = 1. We shall prove that Formula Presented, g, and a modified Formula Presented are bounded form H1(Δ) to L1(Δ).

本文言語English
ホスト出版物のタイトルInfinite Dimensional Harmonic Analysis IV
ホスト出版物のサブタイトルOn the Interplay Between Representation Theory, Random Matrices, Special Functions, and Probability
出版社World Scientific Publishing Co.
ページ158-171
ページ数14
ISBN(電子版)9789812832825
ISBN(印刷版)9812832815, 9789812832818
DOI
出版ステータスPublished - 2008 1月 1
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ASJC Scopus subject areas

  • 数学一般

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