用Bernstein型算子刻划Besov空间
The Description of Besov Spaces with Bernstein Type Operators
Abstract
利用包括Ｂｅｒｎｓｔｅｉｎ 算子，Ｂｅｒｎｓｔｅｉｎ－Ｋａｎｔｏｒｏｖｉｃ算子以及Ｂｅｒｎｓｔｅｉｎ－Ｄｕｒｒｍ ｅｙｅｒ算子的Ｂｅｒｎ－ｓｔｅｉｎ 型算子刻划由ＤｅＶｏｒｅ－Ｙｕ Ｘｉａｎｇｍ ｉｎｇ 引入的一类Ｂｅｓｏｖ 空间，并运用Ｋ－ 泛函与内插空间之间的内在联系，建立刻划这类Ｂｅｓｏｖ 空间特征的等价定理． By using Bernstein operators,Bernstein Kantorovic operators, and Bernstein Durrmeyer operators as well, the problems of simultaneous appoximation in Besov spaces introduced by DeVore and Yu Xiangming are studied. A new type of equivalent theorem of Bernstein type operators is given by using the essential connections between the K functions and the interpolation spaces.