Finite-infinite range inequalities in the complex plane
Let E⫅C be closed, ω be a suitable weight function on E, σ be a positive Borel measure on E. We discuss the conditions on ω and σ which ensure the existence of a fixed compact subset K of E with the following property. For any p, 0<P≤∞, there exist positive constants c1, c2 depending only on E, ω...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000868 |
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| Summary: | Let E⫅C be closed, ω be a suitable weight function on E, σ be a positive
Borel measure on E. We discuss the conditions on ω and σ which ensure the existence of
a fixed compact subset K of E with the following property. For any p, 0<P≤∞, there
exist positive constants c1, c2 depending only on E, ω, σ and p such that for every integer
n≥1 and every polynomial P of degree at most n,
∫E\K|ωnP|pdσ≤c1exp(−c2n)∫K|ωnP|pdσ.
In particular, we shall show that the support of a certain extremal measure is, in some
sense, the smallest set K which works. The conditions on σ are formulated in terms of
certain localized Christoffel functions related to σ. |
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| ISSN: | 0161-1712 1687-0425 |