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Recent Developments in Real and Harmonic Analysis In Honor of Carlos Segovia

:	Carlos Cabrelli, Jose Luis Torrea
:	Carlos Cabrelli, Jose Luis Torrea
:	Recent Developments in Real and Harmonic Analysis In Honor of Carlos Segovia
:	Birkhäuser Basel
:	9780817645885
:	1
:	CHF 85.80
:

:	Analysis
:	English

:	196
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

A collection of invited chapters dedicated to Carlos Segovia, this unified and self-contained volume examines recent developments in real and harmonic analysis. The work begins with a chronological description of Segovia's mathematical life, highlighting his original ideas and their evolution. Also included are surveys dealing with Carlos' favorite topics, and PDE works written by students and colleagues close to Segovia whose careers were in some way influenced by him.

Contributors: H. Aimar, A. Bonami, O. Blasco, L.A. Caffarelli, S. Chanillo, J. Feuto, L. Forzani, C.E. Gutíerrez, E. Harboure, A.L. Karakhanyan, C.E. Kenig, R.A. Macías, J.J. Manfredi, F.J. Martín-Reyes, P. Ortega, R. Scotto, A. de la Torre, J.L. Torrea.

	ANHA Series Preface	7
	Foreword	10
	Preface	12
	Publications of Carlos Segovia	14
	List of Contributors	18
	Contents	20
	Carlos Segovia Fern´andez	22
	1 Square functions	23
	2 Spaces of homogeneous type	27
	3 Weighted inequalities	31
	4 One-sided operators	33
	5 Vector-valued Fourier analysis	34
	6 Harmonic analysis associated with generalized Laplacians	37
	References	41
	Balls as Subspaces of Homogeneous Type: On a Construction due to R. Macías and C. Segovia	46
	1 Introduction	46
	2 Quasi-distance on X and diagonal neighborhoods in X × X	49
	3 Regularization of neighborhoods of .	52
	4 The main result	53
	References	57
	Some Aspects of Vector-Valued Singular Integrals	58
	1 Introduction and notation	58
	2 Theorems and proofs	66
	3 Commutators	71
	Acknowledgement	75
	References	75
	Products of Functions in Hardy and Lipschitz or BMO Spaces	78
	1 Introduction	78
	2 Prerequisites on Hardy and Lipschitz spaces	81
	3 Proofs of Theorem 1.1 and Theorem 1.2	84
	4 Generalization to spaces of homogeneous type	89
	Acknowledgements	91
	References	91
	Harmonic Analysis Related to Hermite Expansions	93
	1 Introduction	93
	2 Hermite polynomials	100
	2.1 The Ornstein–Uhlenbeck maximal operator	101
	2.2 Riesz transforms	107
	2.3 The Littlewood–Paley–Stein functions	108
	3 Hermite functions	110
	3.1 The maximal operator for the heat-diffusion semigroup	111
	3.3 Littlewood–Paley–Stein g functions	113
	Acknowledgements	113
	References	113
	Weights for One–Sided Operators	117
	1 Introduction	117
	2 Weighted Hardy inequalities	119
	3 Weights for the one-sided Hardy–Littlewood maximaloperators	122
	4 Some remarks and properties of the one-sided weights	125
	4.1 Basic weights	125
	4.2 The doubling condition and examples of A+p weights	125
	4.3 The reverse Hölder inequality	126
	4.4 Sharp functions and BMO	127
	5 Some approximations of the identity	130
	6 One-sided singular integrals	132
	6.1 One-sided strongly singular integrals	133
	6.2 One-sided Calderón–Zygmund kernels	134
	6.3 Further examples of one-sided singular kernels	136
	7 Some applications to ergodic theory	140
	7.1 The strong type	141
	7.2 The weak type	143
	7.3 Back to Dunford–Schwartz	145
	8 The one-sided Hardy–Littlewood maximal operator in dimensions greater than 1	146
	Acknowledgements	149
	References	149
	Lectures on Gas Flow in Porous Media	153
	1 Introduction	153
	1.1 Travelling fronts	157
	1.2 Quadratic solution (separation of variables)	157
	1.3 Fundamental solution	157
	2 Scaling	159
	3 Regularity of the free boundary	164
	4 Differentiability of the free boundary	169
	4.1 Blow-up	169
	4.2 Classification of the global solutions	171
	5 Remarks	171
	5.1 N-dimensional results	171
	5.2 Waiting time	172
	5.3 Viscosity solutions	172
	5.4 Global profiles and regularity	174
	5.5 Moving plane method	176
	References	177
	Sharp Global Bounds for the Hessian onPseudo-Hermitian Manifolds	178
	1 Introduction	178
	2 The main theorem	182
	3 Applications to PDE	186
	Acknowledgements	190
	References	190
	Recent Progress on the Global Well-Posednessof the KPI Equation	192
	References	196
	On Monge–Ampère Type Equationsand Applications	198
	1 The Monge–Ampère equation	198
	1.1 Basic facts	198
	1.2 The Dirichlet problem	200
	1.3 Regularity of solutions	201
	1.4 Estimates for the linearized Monge–Ampère equation	203
	2 A Monge–Ampère type equation for reflectors	204
	2.1 Snell’s law	204
	2.2 The reflector problem	204
	2.3 Notion of weak solution for the reflector problem	205
	2.4 Results	206
	Acknowledgements	208
	References	209
	Index	210
	Applied and Numerical Harmonic Analysis	213