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KAKEN_24540191seika.pdf
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Download
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| Title |
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非可換調和解析における特異積分論の新たな展開 : 表現論的手法と実解析的手法の融合
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ヒカカン チョウワ カイセキ ニ オケル トクイ セキブンロン ノ アラタナ テンカイ : ヒョウゲンロンテキ シュホウ ト ジツカイセキテキ シュホウ ノ ユウゴウ
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Hikakan chowa kaiseki ni okeru tokui sekibunron no aratana tenkai : hyogenronteki shuho to jitsukaisekiteki shuho no yugo
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New development in non-commutative harmonic analysis related to singular integrals : a fusion of representation theory and real analysis
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河添, 健
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カワゾエ, タケシ
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Kawazoe, Takeshi
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慶應義塾大学・総合政策学部・教授
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Research team head
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科研費研究者番号 : 90152959
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中井, 英一
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ナカイ, エイイチ
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Nakai, Eiichi
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茨城大学・理学部・教授
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Research team member
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科研費研究者番号 : 60259900
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宮地, 昌彦
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ミヤチ, アキヒコ
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Miyachi, Akihiko
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東京女子大学・現代教養学部・教授
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Research team member
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科研費研究者番号 : 60107696
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Anker, J-Ph.
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Universite d'Orleas, Bâtiment de Mathématiques, 教授
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Research team member
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Koufany, K.
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Universite de Lorraine, 教授
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Research team member
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Peng, L.
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北京大学・数学科学学院・教授
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Research team member
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Lie, Heping
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北京大学・数学科学学院・教授
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Research team member
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Lie, Jianming
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北京大学・数学科学学院・助教授
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Daher, R.
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University Hassan II, Faculty of Sciences, 教授
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Abouelaz, A.
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University Hassan II, Faculty of Science, 教授
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Research team member
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Mejjaoli, H.
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King Faisal University, College of Science, 教授
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Research team member
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2016
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科学研究費補助金研究成果報告書
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2015
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| Abstract |
非可換調和解析の対象として, 主としてヤコビhypergroupにおける特異積分論, とくに最大関数, Littlewood-Paley関数, Lusin面積関数のH1空間における有界性とKunze-Stein現象を扱った。従来の手法はヤコビ変換とその逆変換を用いるものであったが, 本研究ではアーベル変換とその逆変換を用いて行った。最大関数およびLittlewood-Paley関数に関しては, (H1,L1)有界性が得られた。Lusin面積関数に関しては修正型の面積関数の有界性が示された。またKunze-Stein現象の端点評価に関して今回の手法により別証明を与えることができた。
As a target of non-commutative harmonic analysis, mainly, on the Jacobi hyper-group, we investigate (H1,L1) boundedness of maximal functions, Littlewood-Paley's function and Lusin's area function and the Kunze-Stein phenomenon. In conventional approach, we have used the Jacobi transform and its inverse. However, in this research, we use the Abel transform and its inverse. As for maximal functions and Littlewood-Paley's function, we can obtain (H1,L1) boundedness, however, for Lusin's area function we have to modify the function to deduce (H1,L1) boundedness. Although the endpoint estimate of the Kunze-Stein phenomenon was already known, by using the present method, we can give an alternative proof.
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研究種目 : 基盤研究(C)(一般)
研究期間 : 2012～2015
課題番号 : 24540191
研究分野 : 調和解析
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