An exploration of the unity of several areas in harmonic analysis, this text emphasizes real-variable methods. Discusses classical Fourier series, summability, norm convergence, and conjugate function. Examines the Hardy-Littlewood maximal function, the Calderón-Zygmund decomposition, the Hilbert transform and properties of harmonic functions, the Littlewood-Paley theory, more. 1986 edition.
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As an introduction to harmonic analysis for graduate students, Torchinsky (Indiana University) examines the convergence of Fourier series of functions and distributions, then develops the Muckenhoupt theory of A p weights, the Calderon-Zygmund theory of singular integral operators, the Littlewood-Paley theory, and the Fefferman-Stein theory of Hard
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