Papers - Kawazoe, Takeshi

Lp-boundedness of a Hausdorff operator associated with change of variables and weights

KAWAZOE Takeshi, RADOUAN Daher, FAOUAZ Saadi

Scientiae Mathematicae Japonicae 84 ( 3 ) 203 - 212 2021.12

Research paper (scientific journal), Joint Work, Lead author, Accepted,  ISSN  1346-0862

Singular Integral Operators of Convolution Type on Jacobi Hypergroup

Kawazoe T.

Springer Proceedings in Mathematics and Statistics (Springer Proceedings in Mathematics and Statistics)  366   103 - 121 2021

ISSN  21941009

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We shall define a Calderón-Zygmund class CZp(Δα,β) on the Jacobi hypergroup (R+, Δα,β, ∗ ) such that, if a function g on R+ belongs to CZp(Δα,β), then the convolution operator g∗ is bounded from Lq(Δα,β) to itself for p≤ q≤ 2. Actually, we shall obtain a relation between the Lp norms of g and the Abel transform Ag and a transference principle between the Lp operator norms of g∗ and the Euclidean operator ϕ⊛, where ϕ(x)=e(2p-1)ρxAg(x). Therefore, to define the Calderón-Zygmund class CZp(Δα,β), we shall obtain some conditions on g under which ϕ belongs to CZ (R). Then, ϕ⊛ is bounded on Lq(R) and, by the transference principle, g∗ is bounded on Lq(Δα,β).

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An endpoint estimate of the kunze-stein phenomenon on SU(n,m)

Kawazoe T.

Pacific Journal of Mathematics (Pacific Journal of Mathematics)  302 ( 2 ) 645 - 657 2019

ISSN  00308730

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© 2019 Mathematical Sciences Publishers. The endpoint estimates for the Kunze-Stein phenomenon associated with real rank one semisimple Lie groups and the Jacobi hypergroup were obtained by A. Ionescu and J. Liu respectively. Recently, a modified endpoint estimate was also proved for complex semisimple Lie groups by J. Liu and the author. Hence the original estimate seems not to be valid for general semisimple Lie groups with higher rank. We treat the case of SU(n,m) and obtain a modified estimate similarly to the complex case. The process using the Abel transform makes it clear why the original endpoint estimate might not be valid for general semisimple Lie groups.

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Applications of an inverse Abel transform for Jacobi analysis - weak $L^1$ estimates and the Kunze-Stein phenomenon.

KAWAZOE TAKESHI

Tokyo J. Math. 41 ( 1 ) 77 - 112 2018.06

Research paper (scientific journal), Single Work, Accepted

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

Kawazoe T.

Tokyo Journal of Mathematics (Tokyo Journal of Mathematics)  41 ( 1 ) 77 - 112 2018.06

ISSN  03873870

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©2018 International Academic Printing Co. Ltd. All Rights Reserved. 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.

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A modified endpoint estimate of the Kunze-Stein phenomenon associated with complex semisimple Lie groups

KAWAZOE TAKESHI

Scientiae Mathematicae Japonicae    1 - 10 2018.03

Joint Work, Accepted

エレガントな解答をもとむ

KAWAZOE TAKESHI

数学セミナー (日本評論社)  56 ( 6 ) 6 2017.06

関数解析におけるルべ－グ積分

KAWAZOE TAKESHI

数理科学 (サイエンス社)  55 ( 4 ) 56 - 57 2017.04

エレガントな解答をもとむ

KAWAZOE TAKESHI

数学セミナー (日本評論社)  55 ( 7 ) 6 2016.07

Single Work

H1-estimates of the Littlewood-Paley and Lusin functions for Jacobi analysis II

KAWAZOE TAKESHI

Anal. Theory Appl. 32 ( 1 ) 38 - 51 2016.04

Single Work, Accepted

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Inversion formula for the discrete Radon transform

KAWAZOE TAKESHI

Tokyo J. Math. 38   175 - 191 2015.06

Single Work, Accepted

On the Range of the Radon Transform on Zn and the Related Volberg’s Uncertainty Principle.

#HKAWAZOE TAKESHI</>UAbouelaz, Ahmed; Ihsane, Abdallah

Journal of Mathematics. 2015   1 - 9 2015.03

Joint Work

数理統計教育の25年 －慶応義塾大学湘南藤沢キャンパスにおける試み－

KAWAZOE TAKESHI

統計 (日本統計協会)  66 ( 3 ) 26 - 31 2015.03

Single Work

外向きベクトルへの期待

KAWAZOE TAKESHI

数学セミナー (日本評論社)  53 ( 12 ) 1 2014.12

シュルレアリストは数学がお好き

KAWAZOE TAKESHI

数学セミナー (日本評論社)  53 ( 6 ) 1 2014.06

エレガントな解答をもとむ

KAWAZOE TAKESHI

数学セミナー (日本評論社)  52 ( 11 ) 6 2013.11

Joint Work

数セミとの出会いと別れ，そして再会

KAWAZOE TAKESHI

数学セミナー (日本評論社)  52 ( 5 ) 8 2013.05

フーリエ解析と表現論

KAWAZOE TAKESHI

数理科学 (東京：サイエンス社)  51 ( 1 ) 13 - 19 2013.01

Single Work

Generalized Besov spaces and their applications

KAWAZOE TAKESHI

Tokyo J. Math. 35 ( 2 ) 297-320 2012.12

Research paper (scientific journal), Joint Work, Accepted

Nazarov type uncertainty inequality for Fourier series

KAWAZOE TAKESHI

Scientiae Mathematicae Japonicae    177 - 186 2012.08

Research paper (scientific journal), Joint Work, Accepted