$\alpha$-Hölder Integrability Exponent

Abstract

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

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