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2250-18.pdf | 8.7 MB | Adobe PDF | 見る/開く |
タイトル: | ON CHARACTERIZATIONS OF $VMO$$_{¥Delta_{N}}$($¥mathbb{R}$$^{n}$)SPACE (Theory of function spaces and related topics) |
著者: | YABUTA, KÔZÔ |
著者名の別形: | 薮田, 公三 |
キーワード: | Neumann Laplacian VMO spaces Commutator Compactness Riesz transform |
発行日: | May-2023 |
出版者: | 京都大学数理解析研究所 |
誌名: | 数理解析研究所講究録 |
巻: | 2250 |
開始ページ: | 159 |
終了ページ: | 174 |
抄録: | In this note, we shall give a resume of a joint work with Mingming Cao [5]. We state several different characterizations of the vanishing mean oscillation space associated with Neumann Laplacian Δ[N], written VMOΔ[N](ℝ[N]). We first describe it with the classical VMO(ℝ[N]) and certain VMO on the half-spaces. Then we comment that VMOΔ[N](ℝ[N]) is actually BMOΔ[N](ℝ[N])-closure of the space of the smooth functions with compact supports. Beyond that, it can be characterized in terms of the compact commutators of Riesz transforms and fractional integral operators associated to the Neumann Laplacian. Additionally, we by means of the functional analysis obtain the duality between certain VMO and the corresponding Hardy spaces on the half-spaces. Finally, we present an useful approximation for BMO functions on the space of homogeneous type, which can be applied to our argument and otherwhere. |
URI: | http://hdl.handle.net/2433/285461 |
出現コレクション: | 2250 関数空間論とその周辺 |
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