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By Bernard Epstein

This quantity collects six articles on chosen subject matters on the frontier among partial differential equations and spectral idea, written via best experts of their respective box. The articles specialise in subject matters which are within the focal point of present learn, with unique contributions from the authors. they're written in a transparent expository variety that makes them available to a broader viewers. The articles include a close creation and talk about contemporary development, supply extra motivation, and increase the required instruments. additionally, the authors percentage their perspectives on destiny advancements, hypotheses, and unsolved difficulties

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74 (1977), 1324-1327. Chapter 1: Calderon and Zygmund's Theory of Singular Integrals 22 [10] A. P. Calderon and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85-139. [11] [12] , On singular integrals, Amer. J. Math. 78 (1956), 289-309. , Algebras of certain singular integrals, Amer. J. Math. 78 (1956), 310-320. , Singular integral operators and differential equations, Amer. J. Math. 79 (1957), 801-821. [13] [14] A. P. Calderon and R. Vaillancourt, A class of bounded pseudo- differential operators, Proc.

To appear 1999. [19] M. Christ and J. L. Rubio de Francia, Weak-type (1,1) bounds for rough operators II, Invent. Math. 93 (1988), 225-237. [20] R. R. Coifman, A. McIntosh, and Y. Meyer, L'integrale de Cauchy sur les courbes lipschitziennes, Ann. of Math. 116 (1982), 361-387. [21] R. R. Coifman and Y. Meyer, Au-dela des operateurs pseudo-diferentiels, Asterisque no. 57, Societe Math. de France. [22] R. R. Coifman and G. Weiss, Analyse harmonique non-commutative sur certains espaces homogenes, Lecture Notes in Math.

This allows one to transfer information from the dyadic martingales to the differentiation averages and vice versa. References [1] G. D. Birkhoff, Proof of the ergodic theorem, Proc. Nat. Acad. Sci. USA 17 (1931), 656-660. [2] K. Yosida and S. Kakutani, Birkhof's ergodic theorem and the maximal ergodic theorem, Proc. Imp. Acad. Tokyo 15 (1939), 165-168. [3] N. Wiener, The ergodic theorem, Duke Math. J. 5 (1939), 1-18. [4] G. H. Hardy and J. E. Littlewood, A maximal theorem with functiontheoretic applications, Acta Math.

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