Singular integrals on symmetric spaces of real rank one
Ionescu, Alexandru D.
Duke Math. J., Tome 115 (2002) no. 1, p. 101-122 / Harvested from Project Euclid
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In this paper we prove a new variant of the Herz majorizing principle for operators defined by $\mathbb {K}$-bi-invariant kernels with certain large-scale cancellation properties. As an application, we prove $L\sp p$-boundedness of operators defined by Fourier multipliers which satisfy singular differential inequalities of the Hörmander-Michlin type. We also find sharp bounds on the $L\sp p$-norm of large imaginary powers of the critical $L\sp p$-Laplacian.
Publié le : 2002-07-15
Classification:  43A85,  43A32 
@article{1087575358,
     author = {Ionescu, Alexandru D.},
     title = {Singular integrals on symmetric spaces of real rank one},
     journal = {Duke Math. J.},
     volume = {115},
     number = {1},
     year = {2002},
     pages = { 101-122},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087575358}
}

Ionescu, Alexandru D. Singular integrals on symmetric spaces of real rank one. Duke Math. J., Tome 115 (2002) no. 1, pp.  101-122. http://gdmltest.u-ga.fr/item/1087575358/