Department of Mathematics, Macquaire University, New South Wales 2109, Australia, e-mail: lixin@ics.mq.edu.auDepartment of Mathematics, Zhongshan University, Guangzhou 510275, Peoples Republic of China
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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.
[1]Auscher, P., Coulhon, T. and Tchamitchian, Ph., ‘Absence de principle du maximum pour certaines équations paraboliques complexes’, Colloq. Math.171 (1996), 87–95.CrossRefGoogle Scholar
[2]
[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]
[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), 601–606.CrossRefGoogle Scholar
[4]
[4]Auscher, P. and Tchamitchian, Ph., ‘Square root problem for divergence operators and related topics’, Astérisque249 (1998), 577–623.Google Scholar
[5]
[5]Blunck, S. and Kunstmann, P.C., ‘Calderón–Zygmund theory for non-integral operators and H∞ functional calculus’ (to appear).Google Scholar
[6]
[6]Deng, D.G. and Han, Y.S., Theory of Hp spaces (Peking Univ. Press, China, 1992).Google Scholar
[7]
[7]Duong, X.T. and McIntosh, A., ‘Singular integral operators with non-smooth kernels on irregular domains’, Rev. Mat. Iberoamericana15 (1999), 233–265.CrossRefGoogle Scholar
[8]
[8]Liskevich, V., Sobol, Z. and Vogt, H., ‘On Lp-theory of C0-semigroups associated with second order elliptic operators II’ (to appear).Google Scholar
[9]
[9]Liskevich, V. and Vogt, H., ‘On Lp-spectrum and essential spectra of second order elliptic operators’, Proc. London Math. Soc.80 (2000), 590–610.CrossRefGoogle Scholar
[10]
[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. 210–231.Google Scholar
[11]
[11]Stein, E.M., Singular integrals and differentiability properties of functions, Princeton Mathematical Series 30 (Princeton University Press, Princeton N.J., 1970).Google Scholar