The second edition of this book in two volumes: Classical Fourier
Analysis, 2nd Edition, and Modern Fourier Analysis, 2nd Edition. These
volumes are mainly addressed to graduate students who wish to study
Fourier analysis. This second volume is intended to serve as a text for a
seco- semester course in the subject. It is designed to be a
continuation of the rst v- ume. Chapters 1–5 in the rst volume contain
Lebesgue spaces, Lorentz spaces and interpolation, maximal functions,
Fourier transforms and distributions, an introd- tion to Fourier
analysis on the n-torus, singular integrals of convolution type, and
Littlewood–Paley theory. Armed with the knowledgeof this material, in
this volume,the reader encounters more advanced topics in Fourier
analysis whose development has led to important theorems. These theorems
are proved in great detail and their proofs are organized to present
the ow of ideas. The exercises at the end of each section enrich the
material of the corresponding section and provide an opportunity to
develop ad- tional intuition and deeper comprehension.

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