DUOANDIKOETXEA FOURIER ANALYSIS PDF

This formula can be proved using Lemma 1. Notes and further results The classic reference on trigonometric series is the book by Zygmund [21], which will also be a useful reference for results in the next few chap- ters. However, this work can be difficult, to consult at times. Another comprehensive reference on trigonometric series is the book by Bary [1].

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Share this page Javier Duoandikoetxea Fourier analysis encompasses a variety of perspectives and techniques. Motivated by the study of Fourier series and integrals, classical topics are introduced, such as the Hardy-Littlewood maximal function and the Hilbert transform.

The remaining portions of the text are devoted to the study of singular integral operators and multipliers. Chapter 1 presents a review of Fourier series and integrals; Chapters 2 and 3 introduce two operators that are basic to the field: the Hardy-Littlewood maximal function and the Hilbert transform. Chapters 4 and 5 discuss singular integrals, including modern generalizations. Chapter 8 discusses Littlewood-Paley theory, which had developments that resulted in a number of applications.

This volume has been updated and translated from the Spanish edition that was published in It is geared toward graduate students seeking a concise introduction to the main aspects of the classical theory of singular operators and multipliers. Prerequisites include basic knowledge in Lebesgue integrals and functional analysis. Readership Graduate students and research mathematicians interested in Fourier analysis. The students will have a lot to benefit from in the simple and quick presentation of the book.

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Fourier Analysis

Javier Duoandikoetxea writ. Fourier analysis encompasses a variety of perspectives and techniques. Motivated by the study of Fourier series and integrals, classical topics are introduced, such as the Hardy-Littlewood maximal function and the Hilbert transform. The remaining portions of the text are devoted to the study of singular integral operators and multipliers. Chapter 1 presents a review of Fourier series and integrals; Chapters 2 and 3 introduce two operators that are basic to the field: the Hardy-Littlewood maximal function and the Hilbert transform. Chapters 4 and 5 discuss singular integrals, including modern generalizations. Chapter 8 discusses Littlewood-Paley theory, which had developments that resulted in a number of applications.

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