Fourier Analysis (Graduate Studies in Mathematics)

Fourier Analysis (Graduate Studies in Mathematics)

Fourier analysis encompasses a variety of perspectives and techniques. This volume presents the real variable methods of Fourier analysis introduced by CalderÃ³n and Zygmund. The text was born from a graduate course taught at the Universidad AutÃ³noma de Madrid and incorporates lecture notes from a course taught by JosÃ© 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. Both classical aspects of the theory and more recent developments, such as weighted inequalities, $H^1$, $BMO$ spaces, and the $T1$ theorem, are discussed. 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 6 studies the relationship between $H^1$, $BMO$, and singular integrals; Chapter 7 presents the elementary theory of weighted norm inequalities. Chapter 8 discusses Littlewood-Paley theory, which had developments that resulted in a number of applications. The final chapter concludes with an important result, the $T1$ theorem, which has been of crucial importance in the field. This volume has been updated and translated from the Spanish edition that was published in 1995. 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.

Country	USA
Author	Javier Duoandikoetxea
Binding	Hardcover
Brand	Brand: American Mathematical Society
EAN	9780821821725
Feature	Used Book in Good Condition
ISBN	0821821725
IsEligibleForTradeIn	1
Label	American Mathematical Society
Manufacturer	American Mathematical Society
NumberOfItems	1
NumberOfPages	222
PublicationDate	2000-12-12
Publisher	American Mathematical Society
ReleaseDate	2000-10-01
Studio	American Mathematical Society

Fourier Analysis (Graduate Studies in Mathematics)

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