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Harmonic Analysis, Partial Differential Equations, and Related Topics
This collection of contributed articles comprises the scientific program of the fifth annual Prairie Analysis Seminar. All articles represent important current advances in the areas of partial differential equations, harmonic analysis, and Fourier analysis. A range of interrelated topics is presented, with articles concerning Painleve removability, pseudodifferential operators, $A p$ weights, nonlinear Schrodinger equations, singular integrals, the wave equation, the Benjamin-Ono equation, quasi-geostrophic equations, quasiconformal mappings, integral inclusions, Bellman function methods, weighted gradient estimates, Hankel operators, and dynamic optimization problems. Most importantly, the articles illustrate the fruitful interaction between harmonic analysis, Fourier analysis, and partial differential equations, and illustrate the successful application of techniques and ideas from each of these areas to the others.
Harmonic Analysis and Partial Differential Equations
This volume contains the Proceedings of the 9th International Conference on Harmonic Analysis and Partial Differential Equations, held June 11-15, 2012, in El Escorial, Madrid, Spain. Included in this volume is the written version of the mini-course given by Jonathan Bennett on Aspects of Multilinear Harmonic Analysis Related to Transversality. Also included, among other papers, is a paper by Emmanouil Milakis, Jill Pipher, and Tatiana Toro, which reflects and extends the ideas presented in the mini-course on Analysis on Non-smooth Domains delivered at the conference by Tatiana Toro. The topics of the contributed lectures cover a wide range of the field of Harmonic Analysis and Partial Differential Equations and illustrate the fruitful interplay between the two subfields.
Topics in Harmonic Analysis and Ergodic Theory
There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progressions. This text presents a series of essays on the topic.
The Hardy Space H1 with Non-doubling Measures and Their Applications
The present book offers an essential but accessible introduction to the discoveries first made in the 1990s that the doubling condition is superfluous for most results for function spaces and the boundedness of operators. It shows the methods behind these discoveries, their consequences and some of their applications. It also provides detailed and comprehensive arguments, many typical and easy-to-follow examples, and interesting unsolved problems. The theory of the Hardy space is a fundamental tool for Fourier analysis, with applications for and connections to complex analysis, partial differential equations, functional analysis and geometrical analysis. It also extends to settings where the doubling condition of the underlying measures may fail.
Harmonic Analysis, Partial Differential Equations and Applications
This collection of articles and surveys is devoted to Harmonic Analysis, related Partial Differential Equations and Applications and in particular to the fields of research to which Richard L. Wheeden made profound contributions. The papers deal with Weighted Norm inequalities for classical operators like Singular integrals, fractional integrals and maximal functions that arise in Harmonic Analysis. Other papers deal with applications of Harmonic Analysis to Degenerate Elliptic equations, variational problems, Several Complex variables, Potential theory, free boundaries and boundary behavior of functions.
Perspectives in Partial Differential Equations, Harmonic Analysis and Applications
This volume contains a collection of papers contributed on the occasion of Mazya's 70th birthday by a distinguished group of experts of international stature in the fields of harmonic analysis, partial differential equations, function theory, and spectral analysis, reflecting the state of the art in these areas.
Fractal Geometry and Stochastics
Fractal geometry is a new and promising field for researchers from different disciplines such as mathematics, physics, chemistry, biology and medicine. It is used to model complicated natural and technical phenomena. The most convincing models contain an element of randomness so that the combination of fractal geometry and stochastics arises in between these two fields. It contains contributions by outstanding mathematicians and is meant to highlight the principal directions of research in the area. The contributors were the main speakers attending the conference "Fractal Geometry and Stochastics" held at Finsterbergen, Germany, in June 1994. This was the first international conference ever to be held on the topic. The book is addressed to mathematicians and other scientists who are interested in the mathematical theory concerning: • Fractal sets and measures • Iterated function systems • Random fractals • Fractals and dynamical systems, and • Harmonic analysis on fractals. The reader will be introduced to the most recent results in these subjects. Researchers and graduate students alike will benefit from the clear expositions.
50 Years with Hardy Spaces
Written in honor of Victor Havin (1933–2015), this volume presents a collection of surveys and original papers on harmonic and complex analysis, function spaces and related topics, authored by internationally recognized experts in the fields. It also features an illustrated scientific biography of Victor Havin, one of the leading analysts of the second half of the 20th century and founder of the Saint Petersburg Analysis Seminar. A complete list of his publications, as well as his public speech "Mathematics as a source of certainty and uncertainty", presented at the Doctor Honoris Causa ceremony at Linköping University, are also included.
An Introduction to Operators on the Hardy-Hilbert Space
This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.
