On Lp estimates for square roots of second order elliptic operators on ℝn

Publicacions Matematiques

Volumn 48, Issue 1, 2004, Pages 159-186

  Auscher, Pascal ^a  

^a UNIVERSITÉ PARIS SUD   (France)

Author keywords

Calder n Zygmund decomposition; Elliptic operators; Functional calculus; Square roots

Indexed keywords

EID: 2442631307     PISSN: 02141493     EISSN: None     Source Type: Journal    
DOI: 10.5565/PUBLMAT_48104_08     Document Type: Article

References (24)

1. n and related estimates, Preprint 4, Université Paris XI-Orsay (2004).
2. ∞-contractivité pour les semigroupes associés aux opérateurs elliptiques complexes sous forme divergence, Potential Anal. 12(2) (2000), 169-189.
3. n, Ann. of Math. (2) 156(2) (2002), 633-654.
4. n, dedicated to the memory of Tosio Kato, J. Evol. Equ. 1(4) (2001), 361-385.
5. [AMcT] P. AUSCHER, A. MCINTOSH AND PH. TCHAMITCHIAN, Heat kernels of second order complex elliptic operators and applications, J. Funct. Anal. 152(1) (1998), 22-73.
6. [AT1] P. AUSCHER AND PH. TCHAMITCHIAN, Square root problem for divergence operators and related topics, Astérisque 249 (1998), 172 pp.
7. [AT2] P. AUSCHER AND PH. TCHAMITCHIAN, Calcul fontionnel précisé pour des opérateurs elliptiques complexes en dimension un (et applications à certaines équations elliptiques complexes en dimension deux), Ann. Inst. Fourier (Grenoble) 45(3) (1995), 721-778.
8. [BK1] S. BLUNCK AND P. C. KUNSTMANN, Calderón-Zygmund theory for non-integral operators and the H∞ functional calculus, Rev. Mat. Iberoamericana 19(3) (2003), 919-942.
9. [BK2] S. BLUNCK AND P. C. KUNSTMANN, Weak-type (p,p) estimates for Riesz transforms, Math. Z. (to appear).
10. [C] C. P. CALDERÓN, On commutators of singular integrals, Studia Math. 53(2) (1975), 139-174.
11. 2 pour les courbes lipschitziennes, Ann. of Math. (2) 116(2) (1982), 361-387.
12. ∞ functional calculus, J. Austral. Math. Soc. Ser. A 60(1) (1996), 51-89.
13. [Da] E. B. DAVIES, Uniformly elliptic operators with measurable coefficients, J. Funct. Anal. 132(1) (1995), 141-169.
14. [DMc] X. T. DUONG AND A. MCINTOSH, Singular integral operators with non-smooth kernels on irregular domains, Rev. Mat. Iberoamericana 15(2) (1999), 233-265.
15. [ERS] A. F. M. TER ELST, D. W. ROBINSON AND A. SIKORA, On second-order periodic elliptic operators in divergence form, Math. Z. 238(3) (2001), 569-637.
16. [GM] M. GIAQUINTA AND G. MODICA, Regularity results for some classes of higher order nonlinear elliptic systems, J. Reine Angew. Math. 311/312 (1979), 145-169.
17. [HaK] P. HAJŁASZ AND P. KOSKELA, Sobolev met Poincaré, Mem. Amer. Math. Soc. 145(688) (2000), 101 pp.
18. [HMc] S. HOFMANN AND A. MCINTOSH, The solution of the Kato problem in two dimensions, in: "Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations" (El Escorial, 2000), Publ. Mat. Vol. extra (2002), 143-160.
19. p bounds for Riesz transforms and square roots associated to second order elliptic operators, Publ. Mat. 47(2) (2003), 497-515.
20. [K] T. KATO, Fractional powers of dissipative operators, J. Math. Soc. Japan 13 (1961), 246-274.
21. [Ke] C. E. KENIG, "Harmonic analysis techniques for second order elliptic boundary value problems", CBMS Regional Conference Series in Mathematics 83, published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1994.
22. [LeM] C. LE MERDY, Square functions associated to sectorial operators, Bull. Soc. Math. France (to appear).
23. [Mor] C. B. MORREY, JR., "Multiple integrals in the calculus of variations", Die Grundlehren der mathematischen Wissenschaften 130, Springer-Verlag New York, Inc., New York, 1966.
24. [St] E. M. STEIN, "Singular integrals and differentiability properties of functions", Princeton Mathematical Series 30, Princeton University Press, Princeton, N.J., 1970.