This volume presents the real variable methods of Fourier analysis introduced by Calderon and Zygmund. The text was born from a graduate course taught at the Universidad Autonoma de Madrid and incorporates lecture notes from a course taught by Jose Luis Rubio de Francia at the same university. 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.
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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. This volume has been updated and translated from the Spanish edition that was published in Minor changes have been made to the core of the book; however, the sections, "Notes and Further Results" have been considerably expanded and incorporate new topics, results, and references.
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.
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