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MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS ON PRODUCT SPACES
http://hdl.handle.net/10131/5737
http://hdl.handle.net/10131/5737cffda817-0e43-46d5-8f8e-f117fae86e54
名前 / ファイル | ライセンス | アクション |
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YMJ_49_N1_2001_001-015.pdf (1.0 MB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2009-12-15 | |||||
タイトル | ||||||
タイトル | MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS ON PRODUCT SPACES | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | departmental bulletin paper | |||||
著者 |
Ding, Yong
× Ding, Yong× Fan, Dashan× Pan, Yobiao |
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著者所属 | ||||||
Department of Mathematics, Beijing Normal University, Beijing, 100875, RPC | ||||||
著者所属 | ||||||
Department of Mathematics, University of Wisconsin-Milwaukee, MIlwaukee, WI 53201, USA | ||||||
著者所属 | ||||||
Department of Math., University of Pittsburgh, Pittsburgh, PA 15260 USA | ||||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | Suppose that $¥Omega(x^{¥prime}, y^{¥prime})¥in L^{1}(S^{n-1}¥times S^{m-1})$ is ahomogeneous function of degree zero $satis¥Phi ing$ the mean zero propeIty (1.1), and that $h(s,t)$ ls a bounded function on $Rx$ R. The Marcinkiewicz integral operator $m(f)$ along a continuous surface $¥gamma(u, v)$ on the product space $R^{n}xR^{m}(n¥geq 2, m¥geq 2)$ is defined by $¥iota_{O}f(¥xi, ¥eta, z)=(¥int_{R}¥int_{R}|F_{l,¥epsilon}(x, y, z)|^{2}2^{-2t-2¥epsilon}dtds)^{1/2}$ where $F_{t,e}(¥xi, ¥eta, z)$ $=¥int_{|_{¥nu}^{x}|^{:}}<2h(|x|, |y|)|x|^{-n+1}|y|^{-m+1}¥Omega(x^{¥prime}, y^{¥prime})f(¥xi-x,¥eta-y, z-¥gamma(|x|, |y|))dxdy<2$ We prove that the operator $¥nu_{¥Omega}f$ is bounded on $L^{P}(R^{n} xR^{m}xR),$ $p¥in(1, ¥infty)$ , provided that $¥Omega$ is a function in certain block space $B_{q}^{0,1}(S^{n-1}xS^{m-1})$ for some $q>1$ and that two lower dimensional maximal functions related to $¥gamma$ are bounded on $L^{p}$ . These two lower dimensional maximal functions are natural extension of a well-known maximal function along curves. | |||||
書誌情報 |
Yokohama Mathematical Journal = 横濱市立大學紀要. D部門, 数学 巻 49, 号 1, p. 1-15, 発行日 2001 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 00440523 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA0089285X | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
著者版フラグ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
出版者 | ||||||
出版者 | Yokohama City University and Yokohama National University |