Real hardy space for jacobi analysis and its applications

Takeshi Kawazoe

doi:10.1142/9789812832825_0010

Real hardy space for jacobi analysis and its applications

Takeshi Kawazoe

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

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 L^p(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).

Original language	English
Title of host publication	Infinite Dimensional Harmonic Analysis IV: On the Interplay Between Representation Theory, Random Matrices, Special Functions, and Probability
Publisher	World Scientific Publishing Co.
Pages	158-171
Number of pages	14
ISBN (Electronic)	9789812832825
ISBN (Print)	9812832815, 9789812832818
DOIs	https://doi.org/10.1142/9789812832825_0010
Publication status	Published - 2008 Jan 1
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.1142/9789812832825_0010

Cite this

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N2 - 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).

AB - 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).

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ER -

Real hardy space for jacobi analysis and its applications

Abstract

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