Functions in the spaceR2(E)at boundary points of the interior
1983 ◽
Vol 6
(2)
◽
pp. 363-370
Keyword(s):
LetEbe a compact subset of the complex planeℂ. We denote byR(E)the algebra consisting of (the restrictions toEof) rational functions with poles offE. Letmdenote2-dimensional Lebesgue measure. Forp≥1, letRp(E)be the closure ofR(E)inLp(E,dm).In this paper we consider the casep=2. Letx ϵ ∂Ebe a bounded point evaluation forR2(E). Suppose there is aC>0such thatxis a limit point of the sets={y|y ϵ Int E,Dist(y,∂E)≥C|y−x|}. For thosey ϵ Ssufficiently nearxwe prove statements about|f(y)−f(x)|for allf ϵ R(E).
1979 ◽
Vol 2
(3)
◽
pp. 415-426
1983 ◽
Vol 6
(3)
◽
pp. 459-466
1976 ◽
Vol 28
(1)
◽
pp. 112-115
◽
Keyword(s):
1979 ◽
Vol 85
(1)
◽
pp. 61-68
◽
Keyword(s):
1976 ◽
Vol 74
◽
pp. 81-89
Keyword(s):
1986 ◽
Vol 6
(2)
◽
pp. 167-182
◽
2018 ◽
Vol 43
(1)
◽
pp. 137
◽
1943 ◽
Vol 39
(1)
◽
pp. 51-53
Keyword(s):
2000 ◽
Vol 38
(5)
◽
pp. 1409-1424
◽