Article

A new capacity in the class of sh<sub>m</sub> functions defined by laplace operator

Nurali AkramovNational University of Uzbekistan, Tashkent, UzbekistanKhakimboy EgamberganovNational University of Singapore, Singapore

Bulletin of National University of Uzbekistan Mathematics and Natural Sciencesjournal2023en

ABI

Abstract

In this paper, we define a new capacity Δm on the class of shm functions, which is defined by Laplace operator. We prove that Δm-capacity satisfies Choquet’s axioms of measurability. Moreover, we compare our capacity with Sadullaev-Abdullaev capacities. In particular, it implies that Δm-capacity of a set E is zero if and only if E is a m-polar set.

Topics

Analytic and geometric function theory Holomorphic and Operator Theory Aerospace Engineering and Control Systems

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DOI: 10.56017/2181-1318.1255

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A new capacity in the class of sh&lt;sub&gt;m&lt;/sub&gt; functions defined by laplace operator

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A new capacity in the class of sh<sub>m</sub> functions defined by laplace operator