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Harmonic and Analytic Functions Of Several Variables and The Maximal Theorem Of Hardy and Littlewood

Published online by Cambridge University Press:  20 November 2018

H. E. Rauch
H. E. Rauch*
Affiliation:
University of Pennsylvania
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The present paper, an edited excerpt from my dissertation, arose from the suggestion of S. Bochner that I try to extend the maximal theorem of Hardy and Littlewood

(2) to functions analytic in the solid unit hypersphere

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 171 - 183
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Courant, R. and Hilbert, D., Methoden der Mathematischen Physik, vol. II (Berlin, 1937)Google Scholar
2. Hardy, G. H. and Littlewood, J. E., A maximal theorem with function-theoretic applications, Acta Math., 54 (1930), 81–116.Google Scholar
3. Rauch., H. E. Generalisation d'une proposition de Hardy et Littlewood et de théorèmes ergodiques qui s'y rattachent, Comptes Rendus, 227 (1948), 887–889.Google Scholar
4. Rauch., H. E., A Poisson formula and the Hardy and Littlewood theorem for matrix spaces, Bull. Amer. Math. Soc, 55 (1949), Abstract 250.Google Scholar
5. Smith, K. T., A generalization of an inequality of Hardy and Littlewood, Can. J. Math., 8 (1956), 157–170.Google Scholar
6. Wiener, N., The ergodic theorem, Duke Math. J., 5 (1939), 1–18.Google Scholar
7. Zygmund, A., Trigonometrical Series (Warsaw, 1935).Google Scholar
8. Zygmund, A., On the existence of boundary values for regular functions of several complex variables, Bull. Amer. Math. Soc, 54 (1948), Abstract 502t.Google Scholar
9. Zygmund, A., A remark on functions of several complex variables, Acta Szeged, 12 (1950), 66–68.Google Scholar
10. Zygmund, A., On the boundary values of functions of several complex variables, Fund. Math., 86 (1949), 207–305.Google Scholar