李颂孝;Stevo Stevi'c
Li Songxiao; Stevo Stevi'c
摘要:
Let f be a holomorphic function on the unit polydisc Dn, with Taylor expan-
sion
f(z) = ∑∞|k|=0 akzk ≡ ∑∞k1+···+kn=0 ak1,···, knzk11· · · zknn
where k = (k1, · · · , kn) ∈ Zn+. The authors define generalized Hilbert operator on Dn by
Hγ,n(f)(z) =∑∞|k|=0 i1,···,in≥0 ai1,···,in Πnj=1Γ( γj + kj + 1)Γ(kj + ij + 1) /Γ(kj + 1)Γ(kj + ij +γj + 2)zk,
where γ ∈ Cn, such that Rγj > -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 inequality on the weighted Bergman space on Dn and find an invariant space for the generalized Hilbert operator.
中图分类号: