H^p(M)空间的插值性质

Interpolating Theorems of the H^p(M) Spaces

以现代分析方法讨论了Hp(M)空间的插值性质,得到Hp(M)空间是H∞空间与Hp空间的内插空间,得到Hp(M)空间与H∞空间和Hp空间的插值不等式。同时,当整函数M(z)=∑n=1∞anzn,Φ(z)=∑n=1∞bnzn,0≤bpn≤an时,(H∞,Hp,Hp(M))是关于(H∞,Hp,H(Φ))的内插拼三组,从而沟通了Hp(M)空间和Hp(Φ)空间的内插关系。

The paper discusses interpolating properties about Hp（ M） spaces. It is obtained that Hp（ M） spaces was interpolating spaces of H∞spaces and Hpspaces. The interpolating inequations of Hp（ M） spaces,H∞spaces and Hpspaces was obtained. When M（z）=∑n=1∞anzn and Φ（z）=∑n=1∞bnzn both are non-constant entire function,and 0 ≤ bn≤an,then（ H∞,Hp,Hp（ M）） is an interpolation trio with respect to（ H∞,Hp,Hp（ Φ））. It is communicated interpolating linkages of Hp（ M） and Hp（ Φ）.