# Fourier Analysis (Graduate Studies in Mathematics.Volume 29) by Javier Duoandikoetxea PDF

By Javier Duoandikoetxea

ISBN-10: 0821821725

ISBN-13: 9780821821725

Fourier research features a number of views and methods. This quantity offers the true variable equipment of Fourier research brought through Calderón and Zygmund. The textual content used to be born from a graduate path taught on the Universidad Autónoma de Madrid and contains lecture notes from a path taught by way of José Luis Rubio de Francia on the similar college. prompted through the learn of Fourier sequence and integrals, classical themes are brought, similar to the Hardy-Littlewood maximal functionality and the Hilbert remodel. the remainder parts of the textual content are dedicated to the research of singular quintessential operators and multipliers. either classical elements of the speculation and more moderen advancements, reminiscent of weighted inequalities, $H^1$, $BMO$ areas, and the $T1$ theorem, are mentioned. bankruptcy 1 provides a evaluation of Fourier sequence and integrals; Chapters 2 and three introduce operators which are uncomplicated to the sector: the Hardy-Littlewood maximal functionality and the Hilbert remodel. Chapters four and five speak about singular integrals, together with smooth generalizations. bankruptcy 6 reports the connection among $H^1$, $BMO$, and singular integrals; bankruptcy 7 offers the simple thought of weighted norm inequalities. bankruptcy eight discusses Littlewood-Paley conception, which had advancements that led to a few purposes. the ultimate bankruptcy concludes with a huge end result, the $T1$ theorem, which has been of an important value within the box. This quantity has been up to date and translated from the Spanish variation that used to be released in 1995. Minor alterations were made to the middle of the booklet; in spite of the fact that, the sections, "Notes and additional Results" were significantly improved and include new subject matters, effects, and references. it's aimed toward graduate scholars looking a concise advent to the most elements of the classical concept of singular operators and multipliers. necessities comprise easy wisdom in Lebesgue integrals and sensible research.