Author(s): McIntosh A., Portal P. (eds.)
Publisher: Australia
Year: 2006
Language: English
Pages: 139
Preface......Page 3
1 Introduction......Page 4
2 Notation......Page 6
3 A stronger functional calculus for scalar-type spectral operators on certain Banach spaces......Page 7
4 Application to the well-boundedness of sums of operators......Page 10
References......Page 12
1 Introduction......Page 14
2 Probabilistic preliminaries......Page 15
3 Littlewood–Paley decompositions......Page 18
4 Vector-valued Fourier multipliers......Page 20
5 Bootstrapping and induction......Page 23
6 Scope of the two multiplier theorems......Page 24
7 Parabolic theory of multipliers......Page 26
8 Multipliers for Sobolev-type inequalities......Page 27
9 No hyperbolic theory of multipliers......Page 28
Fourier-type......Page 31
Interpolation spaces......Page 32
11 Singular convolution operators......Page 33
12 General Calderón–Zygmund operators......Page 36
References......Page 38
1 Introduction......Page 45
2 Clifford Analysis......Page 48
3 The monogenic spectrum of a complex vector......Page 50
4 Complex Clifford analysis......Page 52
4.1 n odd......Page 56
4.2 n even......Page 58
5 Holomorphic and Monogenic Functions on Sectors......Page 60
6 The analytic functional calculus for systems of operators of type (......Page 63
References......Page 66
1 Introduction......Page 69
2 Defnitions and Notations......Page 70
The operator T......Page 71
The asso* ciated kernel......Page 72
The weak boundedness property......Page 73
Notions from Banach space theory......Page 74
The class RCZO!......Page 75
The weak R-boundedness property......Page 76
3 Proof of Theorem 1.1......Page 77
References......Page 81
1 Introduction......Page 84
2 U-bounded collections of operators......Page 85
3 Sectorial operators......Page 86
4 The main results......Page 89
References......Page 92
1 Introduction......Page 94
2 The wrapping map......Page 95
3 The wrap of Brownian motion......Page 96
4 The wrap of the heat kernel......Page 98
5 Generalisations......Page 99
6 Further directions......Page 100
References......Page 101
1 Introduction......Page 103
3.1 Almost everywhere convergence.......Page 104
3.3 Lebesgue Constants......Page 106
4 Proofs......Page 107
4.1 Proof of 2.1......Page 108
4.2 Menshov’s Result......Page 110
4.3 Proof%%of%%Proposition 2.2......Page 111
References......Page 112
1 Introduction......Page 114
2 Commutators with the di!erentiation operator......Page 118
3.1 The left regular representation......Page 121
References......Page 126
1 Introduction......Page 128
2 Proof of the atomic decomposition......Page 131
References......Page 137
Conference photo
......Page 139
