124 INDEX

|E|, 8

| · |p, 83

ω(r), 48, 105

I, 7

ω(r), 12, 42, 45

ba ω, 84

dA(z), 5

f , 54, 67, 70

fr, 16

fa,p, 25, 55, 64

m(r, f), 46

n(r), 30

n(r, f), 30

vα(r), 6, 7, 11, 13, 16, 47, 53, 54, 80, 104,

111–113

Inv, 8, 9, 15, 29–31, 36–39

associated weight, 14

Bekoll´ e-Bonami weight, 8, 12, 13, 19, 83

Bergman projection, 8

Bergman-Nevanlinna class, 30, 47, 105

Besov space, 83, 93

biharmonic Green function, 18

Bloch space, 49

bounded mean oscillation, 49

Carleson measure, 19, 115

Carleson square, 8

Ces` aro operator, 49

classical non-tangential maximal function,

54

classical weighted Bergman space, 5

conformally invariant, 71, 80

cyclic element, 17

dilatation, 16

Dirichlet type space, 90

distortion function, 6

essentially increasing, 10

exponential weight, 6

factorization, 16, 29, 36, 62

generalized area operator, 116

generalized logarithmic derivative, 106

Hardy space, 5

Hardy-Littlewood maximal function, 20, 66

Hardy-Stein-Spencer identity, 51

harmonic compensator, 18

Horowitz-oscillatory, 111

hyperbolic disc, 8

hyperbolic distance, 8

identity operator, 19

integral operator, 19

interpolating and sampling sequences, 117

invariant subspace, 17

invariant weight, 8, 9, 15, 29–31, 36–39

Jensen’s formula, 30, 31, 40

lacunary series, 45

Laplace operator, 18

linear differential equation, 101–113

Lipschitz space, 66

little Bloch space, 74

Littlewood-Paley, 1, 3, 11, 49, 51–53

logarithmic derivative estimates, 106

M¨ obius invariant, 80

Nevalinna characteristic, 105

non-tangential maximal function, 54, 57,

58, 62, 70, 116

non-tangential region, 14

normal weight, 11

order reduction procedure, 106

oscillatory weight, 7

point evaluation, 84

Poisson kernel, 22

proximity function, 46

pseudohyperbolic disc, 8

pseudohyperbolic distance, 8

radial weight, 5

rapidly decreasing weight, 19, 49, 83

rapidly increasing weight, 6

regular weight, 6

reproducing kernel, 84, 91

Schatten class, 83

Schwarzian derivative, 111

singular value, 83

standard weight, 5

superbiharmonic, 18

tent, 14

Toeplitz operator, 92

trivial inner function, 78

uniformly discrete sequence, 87

univalent function, 17

vanishing mean oscillation, 74

Volterra operator, 49

weight, 5

weight function, 5

weighted Bergman space, 5

weighted maximal function, 20–24, 57, 59,

70, 84