On inequalities with measures of Sobolev type embedding theorems on open sets of the real axis

被引:0
作者
Prokhorov D.V. [1 ]
Stepanov V.D. [1 ]
机构
[1] Computing Center, Far East Division, Russian Academy of Sciences, Khabarovsk
基金
俄罗斯基础研究基金会;
关键词
Embedding theorem; Sobolev space; Weighted Lebesgue space;
D O I
10.1023/A:1016380420615
中图分类号
学科分类号
摘要
We consider some Sobolev-type spaces and obtain a necessary and sufficient condition for their embedding in a Lebesgue space.
引用
收藏
页码:694 / 707
页数:13
相关论文
共 11 条
  • [1] Besov O.V., Il'in V.P., Nikol'skii S., Integral Representations of Functions and Embedding Theorems [in Russian], (1996)
  • [2] Maz'ya V.G., Sobolev Spaces, (1985)
  • [3] Mynbaev K.T., Otelbaev M.O., Weighted Function Spaces and Spectra of Differential Operators [in Russian], (1988)
  • [4] Opic B., Kufner A., Hardy-Type Inequalities, (1990)
  • [5] Maz'ya V.G., On some integral inequalities for functions in several variables, Problems of Mathematical Analysis [in Russian], 3, pp. 33-68, (1972)
  • [6] Oinarov R., On weighted norm inequalities with three weights, J. London Math. Soc., 48, pp. 103-116, (1993)
  • [7] Stepanov V.D., Ushakova E.P., On integral operators with variable integration limits, Trudy Mat. Inst. Steklov., 232, pp. 298-317, (2001)
  • [8] Maz'ya V.G., Parfenov O.G., Two-Weight Criteria of Boundedness for Sobolev Embedding Operator in One-Dimensional Case, (1998)
  • [9] Reed M., Simon B., Functional Analysis [Russian Translation], (1977)
  • [10] Maz'ya V.G., Poborchi S.V., Differentiable Functions on Bad Domains, (1997)