Hardy spaces and divergence operators on strongly Lipschitz domains of ℝn

Journal of Functional Analysis

Volumn 201, Issue 1, 2003, Pages 148-184

  Auscher, Pascal ^a   Russ, Emmanuel ^b  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b AIX MARSEILLE UNIVERSITY   (France)

Author keywords

Atomic decomposition; Boundary condition; Elliptic second order operator; Hardy spaces; Maximal functions; Strongly Lipschitz domain

Indexed keywords

EID: 3042568725     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-1236(03)00059-4     Document Type: Article

References (27)

1. P. Auscher, X.T. Duong, A. McIntosh, Square function estimates, functional calculi and Hardy spaces, in preparation.
2. P. Auscher, P. 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 (3) (1995) 721-778.
3. P. Auscher, P. Tchamitchian, Square Root Problem for Divergence Operators and Related Topics, in: Astérisque, Vol. 249, Society of Mathematics, France, 1998.
4. 1 domains, in: G. Lumer, L. Weis (Eds.), Evolution Equations and their Applications in Physical and Life Sciences, Lecture Notes in Pure and Applied Mathematics, Vol. 215, Marcel Dekker, New York, 2001, pp. 15-32.
5. p theory, Math. Ann. 320 (3) (2001) 577-623.
6. n), Ann. Inst. Fourier (Grenoble) 52 (2002) 1187-1218.
7. n, Forum Math. 6 (1994) 65-81.
8. N, Trans. Amer. Math. Soc. 351 (4) (1999) 1605-1661.
9. N and elliptic boundary value problems, J. Funct. Anal. 114 (1993) 286-347.
10. p, Studia Math. 51 (1974) 269-274.
11. R. Coifman, Y. Meyer, E.M. Stein, Some new function spaces and their applications to harmonic analysis, J. Funct. Anal. 62 (1985) 304-335.
12. R. Coifman, G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977) 569-645.
13. p spaces of several variables, Acta Math. 129 (1972) 137-195.
14. J. Garcia-Cuerva, J.L. Rubio da Francia, Weighted Norm Inequalities and Related Topics, North-Holland Mathematics Studies, Elsevier Science Publishers B.V., Amsterdam, 1985.
15. D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 (1979) 27-42.
16. A. Grigor'yan, Integral maximum principle and its applications, Proc. Roy. Soc. Edinburgh 124A (1994) 353-362.
17. n, Studia Math. 80 (2) (1984) 141-166.
18. n) in terms of atoms, Studia Math. 62 (1) (1978) 93-101.
19. ∞amp; functional calculus, in: Miniconference on Operator Theory and Partial Differential Equations (Canberra), Center for Mathematics and Applications, Vol. 14, Australian National University, Canberra, 1986, pp. 210-231.
20. n, Studia Math. 95 (3) (1990) 205-228.
21. D. Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975) 391-405.
22. S. Semmes, A primer on Hardy spaces, and some remarks on a theorem of Evans and Müller, Comm. Partial Differential Equations 19 (1-2) (1994) 277-319.
23. E.M. Stein, Singular Integrals and Differentiability of Functions, Princeton University Press, Princeton, NJ, 1970.
24. E.M. Stein, Topics in Harmonic Analysis Related to the Littlewood-Paley Theory, Princeton University Press, Princeton, NJ, 1970.
25. E.M. Stein, Harmonic Analysis: Real-variable Methods, Orthogonality and Oscillatory Integrals, Princeton University Press, Princeton, NJ, 1993.
26. p spaces, Acta. Math. 103 (1960) 25-62.
27. H. Triebel, H. Winkelvoß, Intrinsic atomic characterizations of function spaces on domains, Math. Z. 221 (4) (1996) 647-673.