Uniqueness properties of m-subharmonic functions in Cegrell classes

Dieu, Nguyen Quang; Bang, Pham Hien; Hong, Nguyen Xuan

doi:10.1016/j.jmaa.2014.06.008

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Cited by 4 publications

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“…Moreover, this is the largest subset of non-positive m-subharmonic functions defined on Ω for which the complex m−Hessian operator can be continuously extended. The reader is also referred to [7] for another solid development of m−Hessian operator.…”

Section: Introductionmentioning

confidence: 99%

Decay near boundary of volume of sublevel sets of $m-$subharmonic functions

Dieu¹,

Duong²

2020

Preprint

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We investigate decay near boundary of the volume of sublevel sets in Cegrell classes of m− subharmonic function on bounded domains in C n . On the reverse direction, some sufficient conditions for membership in certain Cegrell's classes, in terms of the decay of the sublevel sets, are also discussed. CONTENTS 1. Introduction 1 2. Preliminaries 3 2.1. m-complex Hessian measure 3 2.2. The averaging lemma 4 3. Proofs of the results 6 References 13

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Section: Introductionmentioning

confidence: 99%