- viii, 115 pages : illustrations ; 26 cm.
- Contents: The Hardy-Littlewood maximal operator -- Principal values: some Fourier transforms -- The Calderón-Zygmund theory -- The Littlewood-Paley theory -- Higher Riesz ftransforms -- BMO and H1 -- Singular integrals on other groups -- Interpolation.Includes bibliographical references and index.Summary: "This book, focused on singular integrals, provides basic techniques in real analysis: Hardy-Littlewood maximal operator, Calderon-Zygmund theory, Riesz transforms, Littlewood-Paley theory, Fourier multipliers, spaces H1 and BMO, interpolation of operators (real and complex methods). The subject is rather classical, but we aim at giving a treatment as simple as possible. Despite its concision, this book provides full proofs of all results, not only sketches. At the end of each chapter, a few exercises are proposed with sufficient hints so that a careful reader can solve them. They present materials that would have interrupted the exposition, which nevertheless are important. The prerequisites are: measure and integration theory, a certain familiarity with the Fourier transform in Euclidean spaces"--