Probabilistic Behavior of Harmonic FunctionsBirkhäuser, 6 dec. 2012 - 209 pagini Harmonic analysis and probability have long enjoyed a mutually beneficial relationship that has been rich and fruitful. This monograph, aimed at researchers and students in these fields, explores several aspects of this relationship. The primary focus of the text is the nontangential maximal function and the area function of a harmonic function and their probabilistic analogues in martingale theory. The text first gives the requisite background material from harmonic analysis and discusses known results concerning the nontangential maximal function and area function, as well as the central and essential role these have played in the development of the field.The book next discusses further refinements of traditional results: among these are sharp good-lambda inequalities and laws of the iterated logarithm involving nontangential maximal functions and area functions. Many applications of these results are given. Throughout, the constant interplay between probability and harmonic analysis is emphasized and explained. The text contains some new and many recent results combined in a coherent presentation. |
Din interiorul cărții
Rezultatele 1 - 5 din 32
... nontangential maximal function of u and the Lusin area function of u , respectively . If u is the Poisson extension of a function ƒ on R ” , we will often write Naf and Aaf instead of Nau and Aɑu . The corresponding nontangential ...
... function and the nontangential maximal function are finite or infinite on the same sets . This result also provides a harmonic analysis analogue of Kolmogorov's cele- brated LIL for sequences of independent random variables as well as ...
... nontangential maximal function and Lusin area function will involve sharp estimates which con- trol A by N. These will be obtained in a more straightforward way , that is , we will not need to reduce to the case of martingales ; yet ...
... nontangential maximal functions . 1.5 HP spaces on the upper half space 15 1.6 Some basics on singular integrals 1.7 The g - function and area function 1.8 Classical results on boundary behavior 2223 20 28 31 43 2 Decomposition into ...
... nontangential maximal function and Lusin area function . Our goal is not to give a comprehensive introduction to these topics , but rather to introduce , as quickly and efficiently as possible , the requisite background , both ...
Cuprins
1 | |
An Invariance Principle | 45 |
Kolmogorovs LIL for Harmonic Functions | 63 |
Sharp GoodX Inequalities for A and | 93 |
GoodX Inequalities for the Density of the Area Integral | 135 |
The Classical LILs in Analysis | 173 |
References | 191 |
Subject Index | 200 |
Alte ediții - Afișează-le pe toate
Probabilistic Behavior of Harmonic Functions Rodrigo Banuelos,Charles N. Moore Previzualizare limitată - 1999 |
Probabilistic Behavior of Harmonic Functions Rodrigo Bañuelos,Charles N. Moore Vizualizare fragmente - 1999 |
Probabilistic Behavior of Harmonic Functions Rodrigo Banuelos,Charles N. Moore Nu există previzualizare disponibilă - 2012 |