This article is cited in 14 papers

Integral representations of functions and embeddings of Sobolev spaces on cuspidal domains

D. A. Labutin

Moscow Institute of Physics and Technology

Abstract: Some classes of cuspidal domains $G\in\mathbb R^n$ are introduced, and embeddings of the form $W_p^{(l)}(G)\hookrightarrow L_q(G)$, $l\in\mathbb N$, for Sobolev spaces are established. To this end, estimates of some integral operators are needed. These operators cannot be estimated via Riesz potentials or their anisotropic analogs.

UDC: 517.51

Received: 25.05.1995

DOI: 10.4213/mzm1494

 English version: Mathematical Notes, 1997, 61:2, 164–179

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