Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces

Studia Mathematica

Volumn 168, Issue 1, 2005, Pages 25-50

  Keyantuo, Valentin ^a,b   Lizama, Carlos ^a,c  

^a University of Puerto Rico ^*

^b UNIVERSITY OF PUERTO RICO   (Puerto Rico)

^c UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17044384229     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm168-1-3     Document Type: Article

References (32)

1. H. Amann, Linear and Quasilinear Parabolic Problems, Monogr. Math. 89, Birkhäuser, Basel, 1995.
2. _, On the strong solvability of the Navier-Stokes equations, J. Math. Fluid Mech. 2 (2000), 16-98.
3. W. Arendt, C. Batty and S. Bu, Fourier multipliers for Hölder continuous functions and maximal regularity, Studia Math. 160 (2004), 23-51.
4. W. Arendt, C. J. K. Batty, M. Hieber and F. Neubrander, Vector-Valued Laplace Transforms and Cauchy Problems, Monogr. Math. 96, Birkhauser, Basel, 2001.
5. W. Arendt and S. Bu, The operator-valued Marcinkiewicz multiplier theorem and maximal regularity, Math. Z. 240 (2002), 311-343.
6. _, _, Operator-valued Fourier multipliers on periodic Besov spaces and applications, Proc. Edinb. Math. Soc. (2) 47 (2004), 15-33.
7. 1-BMO duality, in: Probability Theory and Harmonic Analysis (Cleveland, OH, 1983), Monogr. Festbooks Pure Appl. Math. 98, Dekker, New York, 1986, 1-19.
8. _, Vector-valued Hausdorff-Young inequalities and applications, in: Geometric Aspects of Functional Analysis (1986/1987), Lecture Notes in Math. 1317, Springer, Berlin, 1988, 239-249.
9. H. Brézis, Analyse Fonctionnelle. Théorie et Applications, Masson, Paris, 1983.
10. P. L. Butzer and H. Berens, Semi-Groups of Operators and Approximation, Grundlehren Math. Wiss. 145, Springer, New, York, 1967.
11. Ph. Clément and G. Da Prato, Existence and regularity results for an integral equation with infinite delay in a Banach space, Integral Equations Operator Theory 11 (1988), 480-500.
12. Ph. Clément, B. de Pagter, F. A. Sukochev and M. Witvliet, Schauder decompositions and multiplier theorems, Studia Math. 138 (2000), 135-163.
13. B. D. Coleman and M. E. Gurtin, Equipresence and constitutive equations for rigid heat conductors, Z. Angew. Math. Phys. 18 (1967), 199-208.
14. G. Da Prato and A. Lunardi, Periodic solutions for linear integrodifferential equations with infinite delay in Banach spaces, in: Differential Equations in Banach Spaces (Bologna, 1985), Lecture Notes in Math. 1223, Springer, Berlin, 1986, 49-60.
15. _, Solvability on the real line of a class of linear Volterra integrodifferential equations of parabolic type, Ann. Mat. Pura Appl. (4) 150 (1988), 67-117.
16. R. Denk, M. Hieber and J. Prüss, R-boundedness, Fourier multipliers and problems of elliptic and parabolic type, Mem. Amer. Math. Soc. 166 (2003), no. 788.
17. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Grundlehren Math. Wiss. 224, Springer, Berlin, 2nd ed., 1983.
18. M. Girardi and L. Weis, Operator-valued Fourier multiplier theorems on Besov spaces, Math. Nachr. 251 (2003), 34-51.
19. p(X) and geometry of Banach spaces, J. Funct. Anal. 204 (2003), 320-354.
20. V. Keyantuo and C. Lizama, Fourier multipliers and integro-differential equations in Banach spaces, J. London Math. Soc., (2) 69 (2004), 737-750.
21. ∞- functional calculus, in: M. Iannelli, R. Nagel and S. Piazzera (eds.), Functional Analytic Methods for Evolution Equations, Lecture Notes Math. 1855, Springer, Berlin, 2004, 65-311.
22. S. Kwapień, Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients, Studia Math. 44 (1972), 583-595.
23. A. Lunardi, The heat equation with fading memory, SIAM J. Math. Anal. 21 (1990), 1213-1224.
24. S. Monniaux, On uniqueness for the Navier-Stokes system in 3D-bounded Lipschitz domains, J. Funct. Anal. 195 (2002), 1-11.
25. J. W. Nunziato, On heat conduction in materials with memory, Quart. Appl. Math. 29 (1971), 187-204.
26. J. Prüss, Evolutionary Integral Equations and Applications, Monogr. Math. 87, Birkhäuser, Basel, 1993.
27. _, Bounded solutions of Volterra equations, SIAM J. Math. Anal. 19 (1988), 133-149.
28. D. Sforza, Existence in the large for a semilinear integrodifferential equation with infinite delay, J. Differential Equations 120 (1995), 289-303.
29. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Math. Ser. 32, Princeton Univ. Press, Princeton, NJ, 1971.
30. H. Triebel, Theory of Function Spaces, Monogr. Math. 78, Birkhäuser, Basel, 1983.
31. p-regularity, Math. Ann. 319 (2001), 735-758.
32. p-regularity, in: Evolution Equations and Their Applications in Physical and Life Sciences (Bad Herrenalb, 1998), Lecture Notes in Pure and Appl. Math. 215, Dekker, New York, 2001, 195-214.