Poincaré- and Sobolev- type inequalities for complex $m$-Hessian equations

Per Ahag, Rafal Czyz

DOI：: 10.1007/s00025-020-01189-1

英文摘要：

By using quasi-Banach techniques as key ingredient we prove Poincaré- 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 Błocki's integrability conjecture for $m$-subharmonic functions.

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