000			02281nam a22001337a 4500
020			_a9781470409265
082			_a515.2433 _bDUO/F
100			_a Duoandikoetxea, Zuazo, Javier.
245			_a Fourier analysis
260			_aIsland _bAmerican mathematical society _c2013
300			_a222p.
520			_aFourier analysis encompasses a variety of perspectives and techniques. 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 Autónoma de Madrid and incorporates lecture notes from a course taught by José 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-Littlewoods 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, H1, 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-Littlewoods maximal function and the Hilbert transform. Chapters 4 and 5 discuss singular integrals, including modern generalizations. Chapter 6 studies the relationship between H1, BMO and singular integrals, Chapter 7 presents the elementary theory of weighted norm inequalities. Chapter 8 discusses Littlewoods-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.
942			_cBK
999			_c67040 _d67040