矩陣算子作用於貝索夫數列空間與其應用
矩陣算子作用於貝索夫數列空間與其應用
王昆湶
慈濟技術學院醫務管理系
摘 要
在此篇論文中，作者延續探討矩陣算子作用於貝索夫數列空間之間的有界性。若此矩陣算子為對角矩陣，我們能完全的刻畫其有界條件。針對一般的矩陣算子，我們找到了其有界性的充分條件或其必要條件，此必要與充分條件或許不相等。但在某些情況下，充分與必要條件是合而為一的。
利用此結果，我們可應用結論來探討瑕積算子的有界性，此算子是卡德隆-日格瑪算子的一種。
關鍵字與詞：矩陣算子、數列空間、對角矩陣、幾乎對角矩陣、瑕積分算子。
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Matrix Operators Acting on Sequence Spaces of Besov type and Its Applications
Kunchuan Wang
Department of Health Administration, Tzu-Chi College of Technology,
Abstract
In this note, we extend the study of operators with matrix acting on sequence spaces of Besov type. In the diagonal cases, we characterize completely the boundedness of diagonal matrices acting from one sequence space to another sequence space of Besov type. In general cases, we obtain some necessary and some sufficient conditions, which may not be same, for boundedness of matrix operators acting from a sequence space of Besov type to another one. In some special cases, we prove the necessary and the sufficient conditions are coincident. Using these results, we give some applications to paraproduct operators, a special kind of Calderón-Zygmund operators.
Keywords and Phases: Matrix operator, sequence space, diagonal matrix, and almost diagonal matrix.
