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| INVERSE THEOREMS IN $L^{p}$ FOR SOME MULTIDIMENSIONAL POSITIVE LINEAR OPERATORS |
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Citation： |
Zhou Dingxuan.INVERSE THEOREMS IN $L^{p}$ FOR SOME MULTIDIMENSIONAL POSITIVE LINEAR OPERATORS[J].Chinese Annals of Mathematics B,1991,12(4):525~530 |
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Net amount： 767 |
Authors： |
Zhou Dingxuan; |
Foundation： |
Projects by supported by the National Natural Science Foundation of China. |
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| Abstract： |
Let $\[{\{ {L_n}\} _{n \in N}}\]$ be positive linear operators in $\[{L_p}(I),I = [0,1]or[0,\infty )\]$, $I=[0,1]$ or $\[[0,\infty )\]$ This paper considers their variants in $\[{L_p}(I \times I)\]$
$$\[{L_{n,m}}(F;x,y) = {L_n}({L_m}(F(u,v);y);x) = {L_m}({L_n}(F(u,v);x);y),n,m \in N.\]$$
The characterization problem for these operators is solved which gives the inverse theorems in $L_{p}$ for multidimensional Bernstein type operators. |
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