THE GENERALIZED HUA'S INEQUALITY ON THE FOURTH LOO-KENG HUA DOMAIN AND AN APPLICATION

It is well-known that the fourth Loo-keng Hua domain is realized as the form HEIV = {xi(j) is an element of C-Nj, z is an element of R-IV(N) : Sigma(r)(j=1)vertical bar xi(j)vertical bar(2pj) < 1 + vertical bar zz(tau)vertical bar(2) - 2z (z) over bar (tau)}. The following generalized Hua's inequality is proved on HEIV: If (z, xi), (s, zeta) is an element of HEIV, then (1 + vertical bar zz(tau)vertical bar(2) - 2z (z) over bar (tau) - parallel to xi parallel to(2))(1 + vertical bar ss(tau)vertical bar(2) - 2s (s) over bar (tau) - parallel to zeta parallel to(2)) <= (vertical bar 1 + zz(tau)(s) over bar(s) over bar (tau) - 2z (s) over bar (tau)vertical bar - parallel to xi parallel to parallel to zeta parallel to)(2). As an application of this inequality, the boundedness and compactness of the weighted composition operators on Bers-type spaces of the fourth Loo-keng Hua domain are characterized.