$\alpha$-H\"older Integrability Exponent
For a plurisubharmonic function $\varphi$ on $\Omega\subset \mathbb C^n$ we defined $\alpha$-H\"older integrability exponent $c_{\alpha}(\varphi)$ and obtained a lower bound in terms of Lelong number $\nu(\varphi)$ and intersection numbers $e_j(\varphi)$. This lower bound improves the earlier result of Kaufmann \cite{Kf} on the integrability of plurisubharmonic functions with respect to Monge-Amp\'ere measure with $\alpha$-H\"older continuous potentials. We also give a sharp lower bound for $\alpha$-H\"older integrability exponent of certain type of plurisubharmonic functions.
math.CV↗