Square roots of elliptic second order divergence operators on strongly Lipschitz domains: Lp theory

Mathematische Annalen

Volumn 320, Issue 3, 2001, Pages 577-623

  Auscher, P ^a,b   Tchamitchian, Ph ^b,c  

^a UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

^b CNRS   (France)

^c AIX MARSEILLE UNIVERSITY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035612530     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00004487     Document Type: Article

References (21)

1. W. Arendt, A.F.M. ter Elst. Gaussian estimates for second order operators with boundary condition. J. Operator Theory, 38:87-130, 1997
2. P. Auscher, A. McIntosh, A. Nahmod. The square root problem of Kato in one dimension, and first order systems. Indiana Univ. Math. J., 46:659-695, 1997
3. P. Auscher, Ph. Tchamitchian. Calcul fonctionnel précisé pour des opérateurs elliptiques complexes en dimension un (et applications à certaines équations elliptiques complexes en dimension deux). Ann. Inst. Fourier, 45:721-778, 1995
4. P. Auscher, Ph. Tchamitchian. Square root problem for divergence operators and related topics, volume 249 of Astérisque. Soc. Math. France, 1998
5. P. Auscher, Ph. Tchamitchian. An end-point Littlewood-Paley inequality for BVP associated with the Laplacian on Lipschitz domains. Publ. Mat. 43: 685-711 (1999)
6. P. Auscher, Ph. Tchamitchian. Gaussian estimates for second order elliptic operators on Lipschitz and C domains. In Evolution equations and their applications in physical and life sciences, G. Lumer, L. Weis (eds.) Vol. 215 of Lect. Notes in Pure and Applied Mathematics, pp. 15-32. Marcel Dekker, 2001
7. P. Auscher, Ph. Tchamitchian. On square roots of second order elliptic divergence operators on strongly Lipschitz domains and absolutely bounded mean oscillation, mai 1999. Prépublication 1999-12 du LAMFA
8. M. Christ, J.-L. Journé. Polynomial growth estimates for multilinear singular integral operators. Acta Math., 159:51-80, 1987
9. E.B. Davies. Heat kernels and spectral theory. Cambridge Univ. Press, 1992
10. p-spaces. PhD thesis, Mathematics, Physics, Computing and Electronics at Macquarie university, 1990
11. p boundedness of Riesz transforms associated with divergence form operators, 1998. Workshop on Analysis and Applications, Brisbane, 1997, Vol. 37 of Proc. of the CMA, ANU, Canberra, pp. 15-25, 1999
12. A. Grigory'an. Upper bounds of derivatives of the heat kernel on an arbitrary complete manifold. J. Funct. Anal., 127:363-389, 1995
13. M. Grüter, K.-O. Widman. The Green function for uniformly elliptic equations. Manuscripta Math., 37:303-342, 1982
14. D. Jerison, C. Kenig. The inhomogeneous Dirichlet problem in Lipschitz domains. J. Funct. Anal., 130:161-219, 1995
15. n, volume 2 of Mathematical reports. Harwood academic publishers, 1984
16. T. Kato. Perturbation theory for linear operators. Springer Verlag, New York, 1966
17. C. Kenig. Harmonic Analysis techniques for second order elliptic boundary value problems, volume 83 of CBMS - conference lecture notes. AMS, Providence RI, 1995
18. ∞ functional calculus. In Miniconference on operator theory and partial differential equations, volume 14 of Center for Math, and Appl., pages 210-231, Canberra, 1986. Australian National University
19. O. Mendez, M. Mitrea. Complex powers of the Neumann Laplacian in Lipschitz domains. Math. Nach., 1999. To appear
20. E.M. Stein. Singular integrals and differentiability of functions. Princeton University Press, 1970
21. A. Yagi. Coïncidence entre des espaces d'interpolation et des domaines de puissance fractionnaires d'opérateurs. C. R. Acad. Sci. Paris, 299, Série 1:173-176, 1984