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Imbedding C1 into H1

Published online by Cambridge University Press:  20 November 2018

Jingzhi Tie
Jingzhi Tie*
Affiliation:
Department of Mathematics University of Toronto Toronto, Ontario M5SIA1 e-mail: jingzhi@math.toronto.edu
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Abstract

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This article gives a direct proof of Theorem 7.58 of Greiner [4]. This result implies that the classical Mikhlin-Calderón-Zygmund calculus for the principal value convolution operators on ℂ is, in a natural way, the limit of the Laguerre calculus for principal value convolution operators on ℍ1 = ℂ x ℝ.

Keywords

43M80
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 6 , 01 December 1995 , pp. 1317 - 1328
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Beals, R., Gaveau, B., Greiner, P.C. and Vauthier, J., The Laguerre Calculus on the Heisenberg group: II,, Bull. Sci. Math. 110(1986), 225–288.Google Scholar
2. Beals, R. and Greiner, P.C., Calculus on Heisenberg Manifolds, Ann. of Math. Stud. 119, Princeton University Press, Princeton, 1988.Google Scholar
3. Folland, G.B. and Stein, E.M., Estimates for the d b-Complex and Analysis on the Heisenberg Group,, Comm. Pure Appl. Math. 27(1974), 429–522.Google Scholar
4. Greiner, P.C., On the Laguerre Calculus of Left-Invariant Convolution (Pseudo-Differential) Operators on Heisenberg Group, Séminaire Goulaouic-Meyer-Schwartz XI, 1980.1981, 1–39.Google Scholar
5. Greiner, P.C., Imbeding C” into Hn, Proc. Sympos. Pure Math. 43(1985), 133–147.Google Scholar
6. Greiner, P.C. and Stein, E.M., Estimates for the -Neumann Problem, Math. Notes 19, Princeton University Press, Princeton, 1977.Google Scholar
7. Magnus, W., Oberhettinger, F. and Soni, R.P., Formulas and Theorems for the Special Functions of Mathematical Physics, Die Grundlehren Math. Wiss. 52, Springer-Verlag, New York Inc., New York, 1966.Google Scholar
8. Markett, C., Mean Cesaro summability of Laguerre expansion and norm estimates with shifted parameter,, Anal. Math. 8(1982), 19–37.Google Scholar
9. Nagel, A. and Stein, E.M., Lectures on Pseudo-differential operators: Regularity Theorems and Applications to Non-elliptic Problems, Math. Notes 24, Princeton University Press, Princeton, 1979.Google Scholar
10. Peetre, J., The Weyl transform and Laguerre polynomials, Matematiche 27(1972), 301–323.Google Scholar
11. Szegö, G., Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ. 23, Amer. Math. Soc, Providence, Rhode Island, 1939.Google Scholar