Besov空间中Gauss-Weierstrass算子的正逆定理

Direct and Inverse Theorems of Gauss-Weierstrass Operators in Besov Space

在研究关于Gauss-Weierstrass算子的Lp-逼近的基础之上,结合算子范数插值定理,继续研究推导了Gauss-Weierstrass算子在Bp,q^s,Lp上的性质、定理.借助K-泛函,给出Gauss-Weiersttrass算子在Besov空间中的逼近,得出Besov空间中Gauss-Weierstrass算子的正逆定理,并对Besov空间进行刻画.

On the basis of research on the Lp approximation of Gauss-Weierstrass operator,combined with the interpolation theorem of operator norm,the properties and theorems of Gauss-Weierstrass operators in Bp,q^s and Lp are further studied and deduced.By means of K-functional,the approximation of the Gauss-Weiersttrass operator in Besov space is given,and the positive and negative theorems of the Gauss-Weierstrass operator in Besov space are obtained,and the Besov space is described.