Index
A (disk algebra), 35
Abakumov, E., 14, 108
Aleksandrov, A. B., 4-6, 14, 15, 43, 97, 99,
101, 108, 111, 116, 119, 180, 187-189
Aleman, A., 8, 87, 89, 91, 97, 108
Ando, T., 37
annihilator (M±),28
atom, 72
atomic decomposition, 47, 72, 153, 161, 164,
174, 176
Coifman's theorem, 72
Axler, S., 87
B (backward shift operator), 1
backward shift operator
commutant, 109, 188, see also commutant
cyclic vectors, 105, 186, see also cyclic
vectors
definition, 81
invariant subspaces
BMOA, 100
H1,
101
m, 0 p 1, 119
HP,Kp oo, 82
L1/!^, 99
Lpa, 88, 89
VMOA, 99
spectrum, 86, 88, 185, see also o~(I)
Bagemihl, F., 10, 12
balayage (sweep), 90
Bergman space
backward shift invariant subspaces, 88
cyclic vectors for B, 108
definition, 88
dual, 88
Bessaga, C , 37
Beurling, A., 3, 81, 82, 85, 97, 98
Beurling's theorem
for HP, 81
for Smirnov class, 97
Blaschke product, 18
BMO (functions of bounded mean oscilla-
tion), see also bounded mean oscillation
BMOA (analytic functions of bounded mean
oscillation), see also bounded mean os-
cillation
Borel series, 15
bounded mean oscillation
backward shift invariant subspaces, 100
definition, 30
Fefferman duality theorem, 32
John-Nirenberg theorem, 31
Riesz projection operator, 31
truncation, 32
bounded type, 41
Brelot, M., 90
Brown, L., 15
Burkholder, D., 54, 61
Calderon, A., 54
Campanato, S., 66, 160
Carleson, L., 108
C (the cyclic vectors for B), 107
Cauchy integral formula
for Hardy space of the disk, 22
for Hardy space of the upper half plane,
51, 75
Cauchy transform
Aleksandrov's characterization, 26
definition, 23
Fatou's jump theorem, 91
Kolmogorov's theorem, 23
norm, 27
Cg°(R), 62
Coo (extended complex plane), 9
C(T)/zA, 35
C/i (Cauchy transform on a measure), 23
Cohn, W., 109
Coifman, R., 6, 47, 72, 75
Coifman's theorem (on atomic decomposi-
tions), 72
Collingwood, E., 9, 41
commutant
of B o n # 2 n / # f , 111
of B on HP nJf% ( 0 p 1), 189
of B on HP (0 p 1), 188
of B on HP (1 p oo), 111
conjugate Poisson kernel, 52
C+ (upper half plane), 9
C(T) (continuous functions on T), 35
cyclic vectors
for B on Dq, 108
195
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