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On the Exact Values and Bilateral Estimates of Certain Capacities

✍ Scribed by Gennadiy Kalyabin

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
410 KB
Volume
170
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The quantities v(E) of combinatorical nature introduced by YU. V. Netrusov and equivalent to the capacities with respect to generalized Besov and Triebel‐Lizorkin spaces (B~p.q~^(β,N)^(R^n^) and F~p.q~^(β,N)^(R^n^)) are studied.

It is shown that for q = p three exists the fast algorithm of calculating v(E) for E being the arbitrary finite union of elementary bricks.

The simple general upper estimate for capacity of the compact sets is established which appeared to be bilateral for regular structures (such as lattices and convex sets).

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