Weighted norm estimates and maximal regularity

Advances in Differential Equations

Volumn 7, Issue 12, 2002, Pages 1513-1532

  Blunck, S ^a   Kunstmann, P C ^b  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

^b UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011935302     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. H. Amann, "Linear and Quasilinear Parabolic Problems," Birkhäuser 1995.
2. P. Auscher and Ph. Tchamitchian, Square root problem for divergence operators and related topics, Astérisque, 249 (1998), Soc. Math. de France.
3. E. Berkson and T.A. Gillespie, Spectral decompositions and harmonic analysis on UMD spaces, Studia Math., 112 (1994), 13-49.
4. S. Blunck, Maximal regularity of discrete and continuous time evolution equations, Studia Math., 146 (2001), 157-176.
5. p-spaces, J. Funct. Anal., 183 (2001), 211-230.
6. ∞ functional calculus, to appear in Rev. Mat. Iberoam.
7. S. Blunck and P.C. Kunstmann, Weak type (p,p) estimates for Riesz transforms, submitted.
8. S. Blunck and P.C. Kunstmann, Generalized Gaussian estimates and the Legendre transform, in preparation.
9. J. Bourgain, Vector valued singular integrals and the H-BMO duality, Probability Theory and Harmonic Analysis, Dekker 1985, 1-19.
10. T. Coulhon and X.T. Duong, Maximal regularity and kernel bounds: observations on a theorem by Hieber and Prüss, Adv. in Diff. Eq., 5 (2000), 343-368.
11. T. Coulhon and L. Saloff-Coste, Puissances d'un opérateur régularisant, Ann. Inst. H. Poincaré, proba. et stat., 26 (1990), 419-436.
12. E.B. Davies, Uniformly elliptic operators with measurable coefficients, J. Funct. Anal., 132 (1995), 141-169.
13. p-regularity of self-adjoint elliptic operators, J. Diff. Eq., 135 (1997), 83-102.
14. X. T. Duong and A. McIntosh, Functional calculi of second-order elliptic partial differential operators with bounded measurable coefficients, J. Geom. Anal., 6 (1996), 181-205.
15. X.T. Duong and D.W. Robinson, Semigroup kernels, Poisson bounds and holomorphic functional calculus, J. Funct. Anal., 142 (1996), 89-128.
16. C. Fefferman and E.M. Stein, Some maximal inequalities, Amer. J. Math., 93 (1971), 107-115.
17. q-estimates for parabolic evolution equations, Commun. PDE, 22 (1998), 1647-1669.
18. p-regularity, Math. Z., 235 (2000), 559-568.
19. l)- potentials, J. Math. Phys., 22 (1981), 1033-1044.
20. P.C. Kunstmann and H. Vogt, Weighted norm estimates and Lp-spectral independence of linear operators, preprint 2000.
21. D. Lamberton, Equations d'évolution linéaires associées à des semi-groupes de contractions dans les espaces Lp , J. Funct. Anal., 72 (1987), 252-262.
22. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I (Sequence Spaces), Springer 1977.
23. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II (Function Spaces), Springer 1979.
24. V. Liskevich, Z. Sobol, and H. Vogt, On Lp-theory of C0-semigroups associated with second order elliptic operators II, to appear in J. Funct. Anal.
25. V. Liskevich and H. Vogt, On Lp-spectra and essential spectra of second order elliptic operators, Proc. London Math. Soc., 80 (2000), 590-610.
26. A. Lunardi, Analytic semigroups and optimal regularity in parabolic equations, Birkhäuser 1995.
27. G. Schreieck and J. Voigt, Stability of the Lp-spectrum of generalized Schrödinger operators with form small negative part of the potential, "Functional Analysis" Proc. Essen 1991, Bierstedt, Pietsch, Ruess, Vogt eds., Marcel-Dekker, New York, 1994.
28. Z. Sobol and H. Vogt, On Lp-theory of C0-semigroups associated with second order elliptic operators I, preprint 2000.
29. L. Weis, Operator-valued Fourier multiplier theorems and maximal Lp-regularity, Math. Ann., 319 (2001), 735-758.
30. L. Weis, A new approach to maximal regularity, to appear in: Proc. of the "6th International Conference on Evolution Equations and their Applications in Physical and Life Sciences" in Bad Herrenalb 1998, G. Lumer, L. Weis (eds), Marcel Dekker 2000.