Singular integrals on symmetric spaces, II

Ionescu, Alexandru

doi:10.1090/S0002-9947-03-03312-9

Singular integrals on symmetric spaces, II
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by Alexandru D. Ionescu

Trans. Amer. Math. Soc. 355 (2003), 3359-3378

DOI: https://doi.org/10.1090/S0002-9947-03-03312-9

Published electronically: April 25, 2003

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Abstract:

We extend some of our earlier results on boundedness of singular integrals on symmetric spaces of real rank one to arbitrary noncompact symmetric spaces. Our main theorem is a transference principle for operators defined by $\mathbb {K}$-bi-invariant kernels with certain large scale cancellation properties. As an application we prove $L^p$ boundedness of operators defined by Fourier multipliers that satisfy singular differential inequalities of the Hörmander–Michlin type.

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