References
Auscher, P., Regularity theorems and heat kernels for elliptic operators.J. London Math. Soc. (2), 54 (1996), 284–296.
Auscher, P. &Tchamitchian, P.,Square Root Problem for Divergence Operators and Related Topics. Astérisque, 249. Soc. Math. France, Paris, 1998.
Christ, M.,Lectures on Singular Integral Operators. CBMS Regional Conf. Ser. in Math., 77. Conf. Board Math. Sci., Washington, DC, 1990.
Coifman, R. R., Deng, D. G. &Meyer, Y., Domains de la racine carrée de certains opérateurs différentiels accrétifs.Ann. Inst. Fourier (Grenoble), 33 (1983), 123–134.
Coifman, R. R., McIntosh, A. &Meyer, Y., L'intégrale de Cauchy définit un opérateur borné surL 2 pour les courbes lipschitziennes.Ann. of Math. (2), 116 (1982), 361–387.
Coifman, R. R. &Meyer, Y., Nonlinear harmonic analysis, operator theory and P.D.E., inBeijing Lectures in Harmonic Analysis (Beijing, 1984), pp. 3–45. Ann. of Math. Stud., 112. Princeton Univ. Press, Princeton, NJ, 1986.
Dahlberg, B. E. J. &Kenig, C. E.,Harmonic Analysis and Partial Differential Equations. Department of Mathematics, Chalmers University of Technology and the University of Göteborg, Göteborg, 1985.
Dorronsoro, J. R., A characterization of potential spaces.Proc. Amer. Math. Soc., 95 (1985), 21–31.
Fabes, E. B., Jerison, D. S. &Kenig, C. E., Multilinear square functions and partial differential equations.Amer. J. Math., 107 (1985), 1325–1368.
— Necessary and sufficient conditions for absolute continuity of elliptic-harmonic measure.Ann. of Math. (2), 119 (1984), 121–141.
Hofmann, S. &Lewis, J. L.,The Dirichlet Problem for Parabolic Operators with Singular Drift Terms. Mem. Amer. Math. Soc., 151 (719). Amer. Math. Soc., Providence, RI, 2001.
Hofmann, S. & McIntosh, A., The solution of the Kato problem in two dimensions. Unpublished manuscript.
Journé, J.-L., Remarks on Kato's square-root problem, inMathematical Analysis (El Escorial, 1989).Publ. Math., 35 (1991), 299–321.
Kato, T., Fractional powers of dissipative operators.J. Math. Soc. Japan, 13 (1961), 246–274.
— Integration of the equation of evolution in a Banach space.J. Math. Soc. Japan, 5 (1953), 208–234.
Kenic, C. &Meyer, Y., Kato's square roots of accretive operators and Cauchy kernels on Lipschitz curves are the same, inRecent Progress in Fourier Analysis (El Escorial, 1983), pp. 123–143. North-Holland Math. Stud., 111. North-Holland Amsterdam, 1985.
Lacey, M., Personal communication.
Lewis, J. L. &Murray, M. The Method of Layer Potentials for the Heat Equation in Time-Varying Domains. Mem. Amer. Math. Soc., 114 (545). Amer. Math. Soc., Providence, RI, 1995.
McIntosh, A., Square roots of operators and applications to hyperbolic PDEs, inMini-conference on Operator Theory and Partial Differential Equations (Camberra, 1983), pp. 124–136. Proc. Centre Math. Anal. Austral. Nat. Univ., 5. Austral. Nat. Univ., Canberra, 1984.
— On the comparability ofA 1/2 andA *1/2.Proc. Amer. Math. Soc., 32 (1972), 430–434.
— On representing closed accretive sesquilinear forms as (A 1/2 u,A *1/2 v) inNonlinear Partial Differential Equations and Their Applications, Collège de France Seminar, Vol. III (Paris, 1980/1981), pp. 252–267. Res. Notes in Math., 70, Pitman, Boston, MA-London, 1982.
— The square root problem for elliptic operators: a survey, inFunctional-Analytic Methods for Partial Differential Equations (Tokyo, 1989), pp. 122–140. Lecture Notes in Math., 1450. Springer-Verlag, Berlin, 1990.
Author information
Authors and Affiliations
Additional information
Hofmann and Lewis were each partially supported by NSF research grants. Lewis also was partially supported by the Mittag-Leffer Institute, who provided both financial support and a pleasant working atmosphere during the spring of 2000.
Rights and permissions
About this article
Cite this article
Auscher, P., Hofmann, S., Lewis, J.L. et al. Extrapolation of Carleson measures and the analyticity of Kato's square-root operators. Acta Math. 187, 161–190 (2001). https://doi.org/10.1007/BF02392615
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02392615