有界对称域上H^(p,α)空间的性质分析

Analyses on Properties of H^(p,α) Space on Bounded Symmetric Domain

在Cn中的有界对称域上继续分析了Hp,α空间上函数的性质,得到了两个定理。定理1:设0<α<1,0<p<q<∞,β<qαp-βq)-1Mq(r,f)λdr≤C‖f‖λp,α,这里C是与f无关0(1-r)nλ(αp,λ>0,若f∈Hp,α(Ω),那么∫1的正常数。定理2:设0<α<1,0<p<2,β<2αakv(z)∈Hp,α(Ω),那么,∑∞(k+φkvp,若f(z)=∑k,vk=01)np(1+β｜akv｜p<∞。p)

Through continuative probe on the properties of the function on H^(p,α) space in bounded symmetric domain in C^n ,two theorems are obtained.One is to suppose 0<α<1 , 0<p<q<∞ , β<qαp , λ>0 ,if f∈H^(p,α) (Ω),then ∫ ~1_0(1-r)^(nλ(αp-βq)-1)M_q(r,f)~λ d r≤C‖f‖~λ_(p,α),where C is a positive constant which is not correlative with f .The theorem 2 is to suppose 0<α<1 , 0<p<2 , β2αp ,if f(z)= ∑ k,va_(k_v)φ_(k_v)(z)∈H^(p,α)( Ω ), then ∑ ∞k=0(k+1)^(np(1+β2-αp)-n)∑m_kv=1a_(k_v)~p<∞.