We study necessary conditions for compactness of the weighted -Neumann operator on the space for a plurisubharmonic function . Under the assumption that the corresponding weighted Bergman space of entire functions has infinite dimension, a weaker result is obtained by simpler methods. Moreover, we investigate (non)compactness of the -Neumann operator for decoupled weights, which are of the form . More can be said if every defines a nontrivial doubling measure.
"On some spectral properties of the weighted -Neumann operator." Kyoto J. Math. 59 (2) 441 - 453, June 2019. https://doi.org/10.1215/21562261-2019-0013