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On the definition of the Monge-Ampère operator in ℂ2

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Abstract

We show that if u is a plurisubharmonic function defined on an open subset Ω of ℂ2 then the Monge-Ampère measure (dd cu)2 can be well defined if and only if u belongs to the Sobolev space W 1,2 loc (Ω).

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Authors and Affiliations

  1. Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059, Kraków, Poland

    Zbigniew Błocki

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  1. Zbigniew Błocki
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Correspondence to Zbigniew Błocki.

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Partially supported by KBN Grant #2 P03A 028 19

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Błocki, Z. On the definition of the Monge-Ampère operator in ℂ2 . Math. Ann. 328, 415–423 (2004). https://doi.org/10.1007/s00208-003-0491-0

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  • DOI: https://doi.org/10.1007/s00208-003-0491-0

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