Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-07T07:50:14.059Z Has data issue: false hasContentIssue false

A remark on Littlewood–Paley g-function

Published online by Cambridge University Press:  17 April 2009

Lixin Yan
Affiliation:
Department of Mathematics, Macquaire University, New South Wales 2109, Australia, e-mail: [email protected] Department of Mathematics, Zhongshan University, Guangzhou 510275, Peoples Republic of China
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove Lp -estimates for the Littlewood–Paley g-function associated with a complex elliptic operator L = − div A∇ with bounded measurable coefficients in ℝn.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Auscher, P., Coulhon, T. and Tchamitchian, Ph., ‘Absence de principle du maximum pour certaines équations paraboliques complexes’, Colloq. Math. 171 (1996), 8795.CrossRefGoogle Scholar
[2]Auscher, P., Duong, X.T. and McIntosh, A., ‘Boundedness of Banach space valued singular integral operators and Hardy spaces’ (to appear).Google Scholar
[3]Auscher, P., Hofmann, S., Lacey, M., Lewis, J., McIntosh, A. and Tchamitchian, Ph., ‘The solution of Kato's conjectures’, C.R. Acad. Sci. Paris Ser. I Math. 332 (2001), 601606.CrossRefGoogle Scholar
[4]Auscher, P. and Tchamitchian, Ph., ‘Square root problem for divergence operators and related topics’, Astérisque 249 (1998), 577623.Google Scholar
[5]Blunck, S. and Kunstmann, P.C., ‘Calderón–Zygmund theory for non-integral operators and H functional calculus’ (to appear).Google Scholar
[6]Deng, D.G. and Han, Y.S., Theory of Hp spaces (Peking Univ. Press, China, 1992).Google Scholar
[7]Duong, X.T. and McIntosh, A., ‘Singular integral operators with non-smooth kernels on irregular domains’, Rev. Mat. Iberoamericana 15 (1999), 233265.CrossRefGoogle Scholar
[8]Liskevich, V., Sobol, Z. and Vogt, H., ‘On Lp-theory of C 0-semigroups associated with second order elliptic operators II’ (to appear).Google Scholar
[9]Liskevich, V. and Vogt, H., ‘On Lp-spectrum and essential spectra of second order elliptic operators’, Proc. London Math. Soc. 80 (2000), 590610.CrossRefGoogle Scholar
[10]McIntosh, A., ‘Operators which have an H -calculus’, in Miniconference on Operator Theory and Partial Differential Equations (Proceedings of the Centre for Mathematical Analysis,ANU,Canberra,1986), pp. 210231.Google Scholar
[11]Stein, E.M., Singular integrals and differentiability properties of functions, Princeton Mathematical Series 30 (Princeton University Press, Princeton N.J., 1970).Google Scholar