Singular integrals on nilpotent Lie groups
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- by Robert S. Strichartz PDF
- Proc. Amer. Math. Soc. 53 (1975), 367-374 Request permission
Abstract:
Convolution operators $Tf(x) = \smallint f(x{y^{ - 1}})K(y)\;dy$ on a class of nilpotent Lie groups are shown to be bounded on ${L^p},\;1 < p < \infty$, provided the Euclidean Fourier transform of $K$ (with respect to a coordinate system in which the group multiplication is in a special form) satisfies familiar “multiplier” conditions.References
- E. B. Fabes and N. M. Rivière, Singular integrals with mixed homogeneity, Studia Math. 27 (1966), 19–38. MR 209787, DOI 10.4064/sm-27-1-19-38
- Lars Hörmander, Estimates for translation invariant operators in $L^{p}$ spaces, Acta Math. 104 (1960), 93–140. MR 121655, DOI 10.1007/BF02547187
- A. W. Knapp and E. M. Stein, Intertwining operators for semisimple groups, Ann. of Math. (2) 93 (1971), 489–578. MR 460543, DOI 10.2307/1970887
- A. Korányi and S. Vági, Singular integrals on homogeneous spaces and some problems of classical analysis, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 25 (1971), 575–648 (1972). MR 463513
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 367-374
- MSC: Primary 43A22; Secondary 22E30
- DOI: https://doi.org/10.1090/S0002-9939-1975-0420140-6
- MathSciNet review: 0420140