Smoothness properties of functions inR2(x)at certain boundary points
1979 ◽
Vol 2
(3)
◽
pp. 415-426
Keyword(s):
LetXbe a compact subset of the complex planeℂ. We denote byR0(X)the algebra consisting of the (restrictions toXof) rational functions with poles offX. Letmdenote2-dimensional Lebesgue measure. Forp≥1, letRp(X)be the closure ofR0(X)inLp(X,dm).In this paper, we consider the casep=2. Letxϵ∂Xbe both a bounded point evaluation forR2(X)and the vertex of a sector contained inIntX. LetLbe a line which passes throughxand bisects the sector. For thoseyϵL∩Xthat are sufficiently nearxwe prove statements about|f(y)−f(x)|for allfϵR2(X).
1983 ◽
Vol 6
(2)
◽
pp. 363-370
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
◽