二指标二维Lorentz空间的分析性质

Analystic properties of two indexes two dimension Lorentz spaces

将二维Lorentz空间Λ2p(w)推广到二指标二维Lorentz空间Λp2,q(w),给出了当0<r1,r2<∞,0<p,q<∞时,Λr1(u)Λq2,r2(w2),Λ2p,r1(w1)Λq2,r2(w2),Λ2p,r1(w1)Λr2(v)的充要条件,以及当0<r1,0<p,q<∞时,Λp,r1(u)Λq2,∞(w2),Λ2p,r1(w1)Λ2q,∞(w2),Λ2p,r1(w1)Λq,∞(v)的充要条件,研究了二指标二维Lorentz空间和混合Lorentz空间的嵌入关系,并且给出了‖.‖Λ2p,q(w)是拟范数的充要条件等结论.

Two dimension Lorentz spces ∧2^p（ω）are generalized to twoindexes two dimension Lorentz spaces∧2^p·q（ω）.Necessary and sufficient conditions are obtained as ∧^γ1（u）belong to ∧2^p·γ2（ω2）,∧2^p·γ1（ω1） belong to ∧2^p·γ2（ω2）,∧2^p·γ1（ω1） belong to ∧^γ2（v）,when0〈γ1,γ2〈∞,0〈p,p〈∞ and as ∧^p·（v） belong to ∧2^q·∞（ω2）,∧2^p·γ1（ω1）belong to ∧2^q·∞（ω2）,∧2^p·γ1（ω1） belong to ∧^q·∞（v） when 0〈γ1,0〈p,q〈∞.Moreover,embedding relation between two dimension spaces and mixde Lorentz spaces are studied.Furthermore,the necessary and sufficient conditions are contained for∧ 2^p·q（ω）to be quasinormable and so on.