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arXiv · 1908.10135

Poincar\'e- and Sobolev- type inequalities for complex $m$-Hessian equations

Per Ahag·Rafal Czyz
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Abstract

By using quasi-Banach techniques as key ingredient we prove Poincar\'e- and Sobolev- type inequalities for $m$-subharmonic functions with finite $(p,m)$-energy. A consequence of the Sobolev type inequality is a partial confirmation of B\l ocki's integrability conjecture for $m$-subharmonic functions.

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Per Ahag, Rafal Czyz. 2019-08-27. Poincar\'e- and Sobolev- type inequalities for complex $m$-Hessian equations. https://doi.org/10.1007/s00025-020-01189-1

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