Commutative Harmonic Analysis IV: Harmonic Analysis in Rn

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V.P. Khavin, N.K. Nikol'skii
Springer Science & Business Media, Nov 15, 1991 - Mathematics - 228 pages
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In this volume of the series "Commutative Harmonie Analysis", three points mentioned in the preface to the first volume are realized: 1) Multiple Fourier series and Fourier integrals; 2) The machinery of singular integrals; 3) Exeeptional sets in harmonie analysis. The first theme is the subjeet matter of the eontribution by Sh. A. Ali mov, R. R. Ashurov, A. K. Pulatov, whieh in an obvious way eonstitutes the "multidimensional parallel" to S. V. Kislyakov's article in Volume I, devoted to the "inner" questions of Fourier analysis of funetions of one variable. The passage to the analysis of functions defined on ]Rn, n > 1, teIls us something essential about the nature of the problem under study. The eontribution by E. M. Dyn'kin, the beginning of which was already published in Volume I of this subseries, is devoted to singular integrals. Be sides classical material (Calder6n-Zygmund and Littlewood-Paley theory), this article eontains an exposition of reeent results, whieh in an essential way have widened the seope of the whole area and have made it possible to solve many old problems, thereby sometimes transeending the very frames of harmonie analysis in its eanonieal interpretation.

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