The square root problem of kato in one dimension, and first order elliptic systems

Indiana University Mathematics Journal

Volumn 46, Issue 3, 1997, Pages 659-695

  Auscher, Pascal ^a   McIntosh, Alan ^c   Nahmod, Andrea ^b  

^a UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041047691     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.1997.46.1423     Document Type: Article

References (19)

1. D. ALBRECHT, X. T. DUONG AND A. McINTOSH, Operator theory and harmonic analysis, Workshop in Analysis and Geometry 1995, Proceedings of the Centre for Mathematical Analysis. ANU, Canberra (1995).
2. P. AUSCHER, A. McINTOSH AND A. NAHMOD, Holomorphic functional calculi of operators, quadratic estimates and interpolation, Indiana Univ. Math. Journal 46 (1997), 375-403.
3. P. AUSCHER, A. McINTOSH AND PH TCHAMITCHIAN, Heat kernels of second order complex elliptic operators and applications, Journal of Functional Analysis, to appear.
4. P. AUSCHER AND PH. TCHAMITCHIAN, Conjecture de Kato sur des ouverts de ℝ, Rev. Mat. Iberoamericana 8 (1992), 149-201.
5. P. AUSCHER AND PH. TCHAMITCHIAN, Calcul fonctionnel précisé pour des opérateurs elliptiques complexes en dimension un (et applications à certaines équations elliptiques complexes en dimension deux), Annales Institut Fourier 45 (1995), 721-788.
6. A. P. CALDERÓN, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), 1324-1327.
7. ∞ functional calculus, Journal of the Australian Math Society, Series A, 60 (1996), 51-89.
8. R. R. COIFMAN AND Y. MEYER, Fourier analysis of multilinear convolutions, Calderón's theorem, and analysis on Lipschitz curves, Lecture Notes in Mathematics, Springer-Verlag 779 (1980), 104-122.
9. 2 pour les courbes lipschitziennes, Annals of Mathematics 116 (1982), 361-387.
10. G. DAVID, J.-L. JOURNÉ AND S. SEMMES, Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation, Revista Matemática Iberoamericana 1 (1985), 1-56.
11. X. T. DUONG AND D. ROBINSON, Semigroup kernels, Poisson bounds and holomorphic functional calculus, Journal of Functional Analysis 142 (1996), 89-128.
12. TOSIO KATO, Perturbation Theory for Linear Operators, second edition, Springer-Verlag, 1976.
13. C. KENIG AND Y. MEYER, Kato's square roots of accretive operators and Cauchy kernels on Lipschitz curves are the same, Recent Progress in Fourier Analysis, I. Peral ed., Math. Studies 111 (1985), 123-145.
14. J. L. LIONS AND E. MAGENES, Problèmes aux Limites non Homogènes, Vol. I, Dunod, Paris, 1968.
15. YVES MEYER, Ondelettes et Opérateurs, II, Hermann, Paris, 1990.
16. ∞ functional calculus, Miniconference on Operator Theory and Partial Differential Equations, 1986, Proceedings of the Centre for Mathematical Analysis, ANU, Canberra, 14 (1986), 210-231.
17. A. McINTOSH AND A. NAHMOD, Heat kernel estimates and functional calculi of -bΔ, submitted.
18. A. McINTOSH AND T. QIAN, Convolution singular integral operators on Lipschitz curves, Lecture Notes in Mathematics, Springer-Verlag, Proceedings of the Special Year on Harmonic Analysis at Nankai Institute of Mathematics, Tianjin, China, vol. 1494, 1991, pp. 142-162.
19. STEPHEN SEMMES, Square function estimates and the T(b) theorem, Proc. Amer. Math. Soc. 110 (1990), 721-726.