L_p(M)空间的内插性质

Interpolation of L_p(M) Spaces

研究了比幂函数增长得快的N函数所生成的一类Orlicz(奥尔里奇 )函数空间———Lp(M)空间的内插性质 ,得出了Lp(M)空间中线性算子的内插定理 .证明在一些条件下拼三组 (L∞ ,Lp0 ,Lp(M ) )是关于拼三组 (L∞ ,Lp0 ,Lp() )的θ型内插拼三组 .推广了已知的有关Lp(M)空间和经典Lebesgue(勒贝格 )空间的线性算子内插定理 .

The interpolation properties of a class of Orlicz spaces—L p(M) spaces which are generated by some N-functions that increases faster than power functions are studied in this paper.And the interpolation theorems of linear operators in L p(M) spaces are found.Under some conditions,that the trio (L ∞,L p 0,L p(M)) is an interpolation trio with respect to (L ∞,L p 0,L p()) of exponent θ is also proved.This generalized the known result about the interpolation theorem of linear operators in L p(M) spaces and the classical Lebesgue spaces.