Bi-Lipschitz Mappings and Quasinearly Subharmonic Functions

Quasi-Nearly Subharmonicity and Separately Quasi-Nearly Subharmonic Functions

Wiegerinck has shown that a separately subharmonic function need not be subharmonic. Improving previous results of Lelong, Avanissian, Arsove, and of us, Armitage and Gardiner gave an almost sharp integrability condition which ensures a separately subharmonic function to be subharmonic. Completing now our recent counterparts to the cited results of Lelong, Avanissian and Arsove for so-called qu...

Domination Conditions for Families of Quasinearly Subharmonic Functions

Hyperbolically Bi-Lipschitz Continuity for 1/|ω|2-Harmonic Quasiconformal Mappings

We study the class of 1/|w|-harmonic K-quasiconformal mappings with angular ranges. After building a differential equation for the hyperbolic metric of an angular range, we obtain the sharp bounds of their hyperbolically partial derivatives, determined by the quasiconformal constant K. As an applicationwe get their hyperbolically bi-Lipschitz continuity and their sharp hyperbolically bi-Lipschi...

Integrability of Superharmonic Functions and Subharmonic Functions

We apply the coarea formula to obtain integrability of superharmonic functions and nonintegrability of subharmonic functions. The results involve the Green function. For a certain domain, say Lipschitz domain, we estimate the Green function and restate the results in terms of the distance from the boundary.

Semi-hyperbolicity and bi-shadowing in nonautonomous difference equations with Lipschitz mappings

It is shown how known results for autonomous difference equations can be adapted to definitions of semi-hyperbolicity and bi-shadowing generalized to nonautonomous difference equations with Lipschitz continuous mappings. In particular, invertibility and smoothness of the mappings are not required and, for greater applicability, the mappings are allowed to act between possibly different Banach s...