A note on the weighted log canonical thresholds of plurisubharmonic functions
The author gives a condition for the integrability of the expression \[ \int _{\Delta ^n} ||z||^{2t}e^{-2u} dV \] (where \(\Delta ^n\) is the unit polydisc, \(u\) a plurisubharmonic function locally bounded except for the origin, and \(dV\) denotes the Lebesgue measure) in terms of integrals over 1-dimensional (coordinate) slices. As a consequence he gets the following inequality for \(u\) having zero boundary values and the Monge-Ampère mass equal to the Dirac delta at the origin: \[ c_{t+1} (u)\geq c_t (u) +\frac{(n-1)^{n-1} }{c_t (u)^{n-1} } \] where \[ c_t (u)= \sup \big\{ c\geq 0: ||z||^{2t}e^{-2cu} \text{ is integrable near } 0 \big\}. \]
scientific article; zbMATH DE number 6917463
scientific article