Fock型空间上的Carleson测度与正测度符号的Berezin变换（英文）

Fock-Carleson measure and Berezin transform with corresponding positive measure symbols for Fock-type spaces

研究了Fock型空间F_Ψ~p(0<p≤∞)与F_Ψ~q(0<q≤∞)之间的Fock-Carleson测度与对应正测度的Berezin型变换.得到了这些(p,q)-Fock-Carleson测度(0<p≤q≤∞)的有界和消失与对应正测度的Berezin变换有界和在无穷远处消失,均值函数有界和在无穷远处消失分别等价;得到了(p,q)-Fock-Carleson测度(0<q<p≤∞)的有界和消失与对应正测度的Berezin变换属于L^(p/(p-q))(dV),均值函数属于L^(p/(p-q))(dV)等价,其中p=∞时,L^(p/(p-q)(dV))退化为L^1(dV).

In this note, we study Fock-Carleson measures between Fock-type spaces FΨ^p（0〈p≤∞） and FΨ^q（0〈q≤∞）,and Berezin transform wi th corresponding positive measure. Our results show that the -Fock-Carleson measure （0〈p≤q≤∞） is bounded if and only if the Berezin transform with corresponding positive measure is bounded if and only if the mean value function with corresponding positive measure is bounded; the （p ,q）-Fock-Carleson measure （0〈p≤q≤∞） is vanishing i f and only i f the Berezin transform w ith corre-sponding positive measure is vanishing at infinity if and only if the mean value function with corresponding posi-tive measure is vanishing at infinity; the （p,q）-Fock-Carleson measure （0〈p≤q≤∞ ） is bounded i f and only if it is vanishing at infinity if and only if the Berezin transform with corresponding positive measure is in Lp/p-q（dV） if and only if the mean value function wi th corresponding positive measure is in Lp/p-q（dV）, where Lp/p-q（dV） is L^1（dV） when p=∞ .