PROPAGATION OF SMALLNESS FOR SOLUTIONS OF GENERALIZED CAUCHY–RIEMANN SYSTEMS
2004 ◽
Vol 47
(1)
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pp. 191-204
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Keyword(s):
AbstractLet $u$ be a solution of a generalized Cauchy–Riemann system in $\mathbb{R}^n$. Suppose that $|u|\le1$ in the unit ball and $|u|\le\varepsilon$ on some closed set $E$. Classical results say that if $E$ is a set of positive Lebesgue measure, then $|u|\le C\varepsilon^\alpha$ on any compact subset of the unit ball. In the present work the same estimate is proved provided that $E$ is a subset of a hyperplane and the (capacitary) dimension of $E$ is greater than $n-2$. The proof gives control of constants $C$ and $\alpha$.AMS 2000 Mathematics subject classification: Primary 31B35. Secondary 35B35; 35J45
1997 ◽
Vol 07
(02)
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pp. 423-429
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1978 ◽
Vol 26
(1)
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pp. 65-69
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Keyword(s):
1984 ◽
Vol 92
(1)
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pp. 45-45
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1986 ◽
Vol 6
(2)
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pp. 167-182
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2019 ◽
Vol 2019
(751)
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pp. 289-308
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Keyword(s):