Index
ACL (absolutely continuous on lines), 5
a-convex, 159, 161
aD, 35, 35-38, 144-148
adm, 6
admissible density, 6
Agard, S. B., 11
Ahlfors, L. V ., 3, 6, 7, 19 , 22, 23, 25, 27,
34, 35, 43, 61 , 85, 90, 95, 108-110, 114 ,
146
Alestalo, P., 24
Anderson, G. D., 11 , 48
Apollonian metric, 35, 35-38, 144-148
Astala, K., 3, 11, 15, 62, 66, 67, 79, 81, 109,
123-125
B^3 , 94
B, 3
B(z,r), 3
B(D), 87
BMO (bounded mean oscillation), 69
BMO-extension domain, 71, 138 , 139
BMO-norm, 65
Beardon, A. F., 15, 35
Becker, J., 62
Bers, L., 6
Beurling, A., 6, 43, 108-110
bilipschitz extension, 63
bilipschitz extension property, 74
bilipschitz mapping
Euclidean, 21, 94, 127
hyperbolic, 22, 109
Bloch function, 87
Bojarski, B., 6
Bonk, M., 87
Brechner, B., 91
Calvis, D., 62
Carleson, L., 16
chordal metric, 3
comparable Dirichlet integral property, 90
complex derivative, 5
conformal invariant, 34
conformally equivalent, 33
conjugate (quadrilaterals), 48
169
conjugate quadrilateral inequality, 49, 52,
55, 107-110
cross ratio, 25, 47, 52
d"', 81
8"', 81
diam, 22
dilatation
complex, 5
linear, 3
distance-ratio metric, 35, 35-38, 87,
138 - 144
doubling (domain), see harmonic doubling
condition
Duren, P ., 121, 122
ED(u), 71
elliptic integral, 4 7
Erkama, T., 73, 91, 92
extremal distance property, 51, 158- 161
extremal length, 6
fz, 5
Jz, 5
Fatou set, 16
Fefferman, C., 69
Fernandes, J. L., 46, 51, 52, 150, 151
finite Dirichlet energy, 71
Flinn, B. B., 52
Gamelin, T. W., 16
Garnett, J. B., 43, 52, 69, 84
Gol'dstein, V. M., 72
H , 3
hD, 22, 34, 34-38, 138-148
Ht(in Rn), 94
Ht(z), 3
h1,4
Hag, P., 79, 81
half-plane, 3
half-strip, 13, 70, 72, 75, 87
Hamilton, D., 46, 150, 151
Hardy, G. H., 78
Hardy-Littlewood property, 79, 80