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City Campus 
515.43 PEYR

Available

 Description
 viii, 115 pages : illustrations ; 26 cm.
 Notes
 Contents: The HardyLittlewood maximal operator  Principal values: some Fourier transforms  The CalderónZygmund theory  The LittlewoodPaley 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: HardyLittlewood maximal operator, CalderonZygmund theory, Riesz transforms, LittlewoodPaley 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"