GENERALIZED HILBERT OPERATOR AND FEJR-RIESZ TYPE INEQUALITIES ON THE POLYDISC  

作　　者：李颂孝 Stevo Stevi 

机构地区：[1]Department of Mathematics, Jiaying University [2]Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 36/III

出　　处：《Acta Mathematica Scientia》2009年第1期191-200,共10页数学物理学报（B辑英文版）

基　　金：Supported by the NNSF of China(10671115);grants from Specialized Research Fund for the doctoral program of Higher Education(20060560002);NSF of Guangdong Province(7300614)

摘　　要：Let f be a holomorphic function on the unit polydisc Dn,with Taylor expansion f(z) = ∞ |k|=0 akzk ≡ ∞ (k1+···+kn=0) (ak1,···,kn zk1 1znkn)where k = (k1, , kn) ∈ Z+n. The authors define generalized Hilbert operator on Dn by Hγ,n(f)(z) = ∞ |k|=0 i1,···,in≥0 ai1,···,in n j=1 Γ(γj + kj + 1)Γ(kj + ij + 1) Γ(kj + 1)Γ(kj + ij + γj + 2) zk,where γ ∈ Cn, such that R γj > -1, j = 1, 2, , n. An upper bound for the norm of the operator on Hardy spaces Hp(Dn) is found. The authors also present a Fejér-Riesz type ineq...Let f be a holomorphic function on the unit polydisc Dn,with Taylor expansion f(z) = ∞ |k|=0 akzk ≡ ∞ (k1+···+kn=0) (ak1,···,kn zk1 1znkn)where k = (k1, , kn) ∈ Z+n. The authors define generalized Hilbert operator on Dn by Hγ,n(f)(z) = ∞ |k|=0 i1,···,in≥0 ai1,···,in n j=1 Γ(γj + kj + 1)Γ(kj + ij + 1) Γ(kj + 1)Γ(kj + ij + γj + 2) zk,where γ ∈ Cn, such that R γj > -1, j = 1, 2, , n. An upper bound for the norm of the operator on Hardy spaces Hp(Dn) is found. The authors also present a Fejér-Riesz type ineq...

关 键 词：Generalized Hilbert operator Fejé r-Riesz inequality a-Bloch space 

分 类 号：O177[理学—数学]