Błocki’s L^p-integrability conjecture for m-subharmonic functions

Determine whether every m-subharmonic function on a bounded domain in C^n, for 1 ≤ m ≤ n, is locally L^p-integrable for all exponents p with p < nm/(n−m), as conjectured by Błocki.

Background

The paper emphasizes that integrability properties of m-subharmonic functions differ markedly from those of plurisubharmonic functions: while plurisubharmonic functions are locally L^p integrable for any p > 0, m-subharmonic functions do not necessarily share this property.

Within this context, Błocki formulated a conjecture specifying the optimal range of L^p exponents for m-subharmonic functions, namely p < nm/(n−m). The authors note that only partial confirmations exist, underscoring that the full conjecture remains unresolved.