By Loukas Grafakos
The basic objective of those volumes is to provide the theoretical starting place of the sector of Euclidean Harmonic research. the unique version was once released as a unmarried quantity, yet as a result of its dimension, scope, and the addition of recent fabric, the second one version contains volumes. the current version encompasses a new bankruptcy on time-frequency research and the Carleson-Hunt theorem. the 1st quantity includes the classical issues comparable to Interpolation, Fourier sequence, the Fourier remodel, Maximal capabilities, Singular Integrals, and Littlewood-Paley concept. the second one quantity includes more moderen themes corresponding to functionality areas, Atomic Decompositions, Singular Integrals of Nonconvolution sort, and Weighted Inequalities.
These volumes are generally addressed to graduate scholars in arithmetic and are designed for a two-course series at the topic with extra fabric integrated for reference. the necessities for the 1st quantity are passable crowning glory of classes in actual and intricate variables. the second one quantity assumes fabric from the 1st. This e-book is meant to offer the chosen themes extensive and stimulate additional examine. even if the emphasis falls on actual variable tools in Euclidean areas, a bankruptcy is dedicated to the basics of study at the torus. This fabric is integrated for historic purposes, because the genesis of Fourier research are available in trigonometric expansions of periodic services in different variables.
About the 1st edition:
"Grafakos's booklet is especially straightforward with various examples illustrating the definitions and ideas... The remedy is punctiliously sleek with unfastened use of operators and sensible research. Morever, not like many authors, Grafakos has basically spent loads of time getting ready the exercises."
- Kenneth Ross, MAA Online