This article is cited in 4 papers

The structure of compact sets generating normal domains and removable singularities for the space $L_p^1(D)$

V. A. Shlyk

Far Eastern National University

Abstract: A study is made of the properties of $p$-normal domains in $R^n$ ($1<p<+\infty$), which will be minimal in the Köbe sense or normal in the Grötzsch sense when $n=p=2$. Descriptions are obtained of removable singularities for the space $L_p^1(D)$ and for compact sets generating $p$-normal domains, in terms of the theory of contingencies and $(n-1)$-dimensional bi-Lipschitz $NC_p$-compact sets.

UDC: 517.5

MSC: Primary 32D20, 30C20; Secondary 31B15, 30C60, 46E35, 49E10

Received: 03.11.1988 and 19.01.1990

 English version: Mathematics of the USSR-Sbornik, 1992, 71:2, 405–418

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