This book mainly deals with the Bochner–Riesz means of multiple Fourier integral and series on Euclidean spaces. It aims to give a systematical introduction to the fundamental theories of the Bochner–Riesz means and important achievements attained in the last 50 years. For the Bochner–Riesz means of multiple Fourier integral, it includes the Fefferman theorem which negates the Disc multiplier conjecture, the famous Carleson-Sjölin theorem, and Carbery-Rubio de Francia-Vega's work on almost everywhere convergence of the Bochner–Riesz means below the critical index. For the Bochner–Riesz means of multiple Fourier series, it includes the theory and application of a class of function space generated by blocks, which is closely related to almost everywhere convergence of the Bochner–Riesz means. In addition, the book also introduce some research results on approximation of functions by the Bochner–Riesz means.
