Duality of Hardy and BMO spaces associated with operators with heat kernel bounds

Journal of the American Mathematical Society

Volumn 18, Issue 4, 2005, Pages 943-973

  Duong, Xuan Thinh ^a   Yan, Lixin ^b  

^a MACQUARIE UNIVERSITY   (Australia)

^b SUN YAT SEN UNIVERSITY   (China)

Author keywords

BMO; Carleson measure; Hardy space; Holomorphic functional calculi; Schr dinger operator; Second order elliptic operator; Semigroup; Tent space

Indexed keywords

EID: 26844560171     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0894-0347-05-00496-0     Document Type: Article

References (37)

1. n, Annals of Math., 156 (2002), 633-654. MR1933726 (2004c:47096c)
2. P. Auscher and P. Tchamitchian, Calcul fonctionnel précisé pour des opérateurs elliptiques complexes en dimension un (et applications à certaines équations elliptiques complexes en dimension deux), Ann. Institut Fourier (Grenoble), 45 (1995), 721-778. MR1340951 (96f:35036)
3. P. Auscher and P. Tchamitchian, Square root problem for divergence operators and related topics, Asterisque, 249, Soc. Math. France, 1998. MR1651262 (2000c:47092)
4. P. Auscher, X.T. Duong and A. McIntosh, Boundedness of Banach space valued singular integral operators and Hardy spaces, preprint, 2004.
5. T. Coulhon and X.T. Duong, Maximal regularity and kernel bounds: Observations on a theorem by Hieber and Prüss, Adv. Differential Equations, 5 (2000), 343-368. MR1734546 (2001d:34087)
6. ∞ functional calculus, J. Austral. Math. Soc. Ser. A, 60 (1996), 51-89. MR1364554 (97d:47023)
7. R.R. Coifman, Y. Meyer and E.M. Stein, Un nouvel éspace adapté à l'étude des opérateurs définis par des intégrales singuliéres, in "Proc. Conf. Harmonic Analysis, Cortona", Lecture Notes in Math., Vol. 992, pp. 1-15, Springer-Verlag, Berlin/New York, 1983. MR0729344 (85j:42032)
8. R.R. Coifman, Y. Meyer and E.M. Stein, Some new functions and their applications to harmonic analysis, J. Funct. Analysis, 62(1985), 304-335. MR.0791851 (86i:46029)
9. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc., 83 (1977), 569-645. MR0447954 (56:6264)
10. E.B. Davies, Heat kernels and spectral theory, Cambridge Univ. Press, 1989. MR0990239 (90e:35123)
11. D.G. Deng, On a generalized Carleson inequality, Studia Math., 78 (1984), 245-251. MR0782661 (86h:42033)
12. D.G. Deng, X.T. Duong, A. Sikora and L.X. Yan, Comparison between the classical BMO and the BMO spaces associated with operators and applications, preprint, (2005).
13. J. Dziubański, G. Garrigós, T. Martínez, J. Torrea and J. Zienkiewicz, BMO spaces related to Schrödinger operators with potentials satisfying a reverse Hölder inequality, Math. Z., 249 (2005), 329-356. MR2115447.
14. X.T. Duong and A. McIntosh, Singular integral operators with non-smooth kernels on irregular domains, Rev. Mat. Iberoamericana, 15 (1999), 233-265. MR1715407 (2001e:42017a)
15. X.T. Duong and D.W. Robinson, Semigroup kernels, Poisson bounds, and holomorphic functional calculus, J. Funct. Anal., 142 (1996), 89-128. MR1419418 (97j:47056)
16. X.T. Duong and L.X. Yan, New function spaces of BMO type, the John-Nirenberg inequality, interpolation and applications, to appear, Comm. Pure Appl. Math., (2005).
17. J. Dziubański and J. Zienkiewicz, Hardy spaces associated with some Schrödinger operator, Studia Math., 126 (1997), 149-160. MR1472695 (98k:42029)
18. C. Fefferman, Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc., 77 (1971), 587-588. MR0280994 (43:6713)
19. C. Fefferman and E.M. Stein, HP spaces of several variables, Acta Math., 129 (1972), 137-195. MR0447953 (56:6263)
20. p bounds for Riesz transforms and square roots associated to second order elliptic operators, Pub. Mat., 47 (2003), 497-515. MR2006497 (2004i:35067)
21. J.L. Journé, Calderón-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderón. Lecture Notes in Mathematics, 994. Springer, Berlin-New York, 1983. MR0706075 (85i:42021)
22. F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math., 14(1961), 415-426. MR0131498 (24:A1348)
23. P. Li, Harmonic sections of polynomial growth, Math. Research Letters, 4 (1997), 35-44. MR1432808 (981:53054)
24. P. Li and J.P. Wang, Counting dimensions of L-harmonic functions, Ann. of Math., 152 (2000), 645-658. MR1804533 (2002c:58032)
25. J.M. Martell, Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications, Studia Math., 161(2004), 113-145. MR2033231 (2005b:42016)
26. ∞-calculus, Miniconference on operator theory and partial differential equations, (1986) Proc. Centre Math. Analysis, ANU, Canberra 14 (1986), 210-231. MR0912940 (88k:47019)
27. S. Semmes, Square function estimates and the T(b) theorem, Proc. Amer. Math. Soc., 110 (1990), 721-726. MR1028049 (91h:42018)
28. p estimates for Schrödinger operators with certain potentials, Ann. Institut Fourier (Grenoble), 45 (1995), 513-546. MR1343560 (96h:35037)
29. Z. Shen, On fundamental solutions of generalized Schrödinger operators, J. Funct. Anal., 167 (1999), 521-564. MR1716207 (2000j:35055)
30. E.M. Stein, Singular integral and differentiability properties of functions, Princeton Univ. Press, 30, (1970). MR0290095 (44:7280)
31. E.M. Stein, Harmonic analysis: Real variable methods, orthogonality and oscillatory integrals, Princeton Univ. Press, Princeton, NJ, (1993). MR1232192 (95c:42002)
32. E.M. Stein and G. Weiss, On the theory of harmonic functions of several variables I, The theory of HP spaces, Acta Math., 103 (1960), 25-62. MR0121579 (22:12315)
33. W.A. Strauss, Partial differential equations: An introduction. John Wiley & Sons, Inc., New York, 1992. MR1159712 (92m:35001)
34. A. Torchinsky, Real-variable methods in harmonic analysis, Pure and Applied Math., Vol 123, Academic Press, (1986). MR0869816 (88e:42001)
35. L.X. Yan, Littlewood-Paley functions associated to second order elliptic operators, Math. Z., 246 (2004), 655-666. MR2045834 (2005a:42015)
36. K. Yosida, Functional Analysis (fifth edition), Springer-Verlag, Berlin, 1978. MR0500055 (58:17765)
37. Y.P. Zhu, Area functions on Hardy spaces associated to Schrödinger operators, Acta Math. Sci. Ser. B Engl. Ed., 23 (2003), 521-530. MR2032556 (2004k:42029)