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The Hardy Space H1 on Manifolds and Submanifolds

Published online by Cambridge University Press:  20 November 2018

Robert S. Strichartz
Robert S. Strichartz*
Affiliation:
Cornell University, Ithaca, New York
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It is well-known that the space L1(Rn) of integrable functions on Euclidean space fails to be preserved by singular integral operators. As a result the rather large Lp theory of partial differential equations also fails for p = 1. Since L1 is such a natural space, many substitute spaces have been considered. One of the most interesting of these is the space we will denote by H1(Rn) of integrable functions whose Riesz transforms are integrable.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 5 , October 1972 , pp. 915 - 925
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Calderón, A. P., Lebesgue spaces of differentiable functions and distributions, Symp. on Pure Math. 5 (1961), 33–49.Google Scholar
2. Fefferman, C., Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971), 587–588.Google Scholar
3. Nirenberg, L., Pseudo-differential operators, Proc. Symp. Pure Math. 16 (1970), 149–167.Google Scholar
4. Peetre, J., Sur les espaces de Besov, C.R. Acad. Sci. Paris Sér. A-B 264 (1967), A281-A283.Google Scholar
5. Seeley, R. T., Singular integrals and boundary value problems, Amer. J. Math. 88 (1966), 781–809.Google Scholar
6. Stein, E. M., Singular integrals and differentiability properties of functions (Princeton University Press, 1970).Google Scholar
7. Stein, E. M., The characterization of functions arising as potentials. II, Bull. Amer. Math. Soc. 68 (1962), 577–582.Google Scholar
8. Strichartz, R., Boundary values of solutions of elliptic equations satisfying Hp conditions (to appear in Trans. Amer. Math. Soc).Google Scholar