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RIESZ TRANSFORM ESTIMATES IN THE ABSENCE OF A PRESERVATION CONDITION AND APPLICATIONS TO THE DIRICHLET LAPLACIAN

Published online by Cambridge University Press:  08 March 2016

JOSHUA PEATE*
Affiliation:
Department of Mathematics, Macquarie University, North Ryde, NSW 2113, Australia email joshua.peate@mq.edu.au
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Abstract

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Type
Abstracts of Australasian PhD Theses
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Auscher, P., Coulhon, T., Duong, X.-T. and Hofmann, S., ‘Riesz transform on manifolds and heat kernel regularity’, Ann. Sci. Éc. Norm. Supér. (4) 37(6) (2004), 911957.CrossRefGoogle Scholar
Auscher, P. and Martell, J. M., ‘Weighted norm inequalities, off-diagonal estimates and elliptic operators. II: off-diagonal estimates on spaces of homogeneous type’, J. Evol. Equ. 7(2) (2007), 265316.Google Scholar
Coulhon, T. and Duong, X.-T., ‘Riesz transforms for 1 ≤ p ≤ 2’, Trans. Amer. Math. Soc. 351(3) (1999), 11511169.CrossRefGoogle Scholar
Gyrya, P. and Saloff-Coste, L., Neumann and Dirichlet Heat Kernels in Inner Uniform Domains (Société Mathématique de France, Paris, 2011).Google Scholar
Killip, R., Visan, M. and Zhang, X., ‘Riesz transforms outside a convex obstacle’, Int. Math. Res. Notices 2015 (2015), doi:10.1093/imrn/rnv338.Google Scholar
Li, P. and Yau, S. T., ‘On the parabolic kernel of the Schrödinger operator’, Acta Math. 156 (1986), 154201.CrossRefGoogle Scholar
Song, R., ‘Estimates on the Dirichlet heat kernel of domains above the graphs of bounded C 1, 1 functions’, Glas. Mat. Ser. III 39(2) (2004), 273286.CrossRefGoogle Scholar
Strichartz, R. S., ‘Analysis of the Laplacian on a complete Riemannian manifold’, J. Funct. Anal. 52 (1983), 4879.Google Scholar
Zhang, Q. S., ‘The global behavior of heat kernels in exterior domains’, J. Funct. Anal. 200(1) (2003), 160176.CrossRefGoogle Scholar