Maximal regularity for perturbed integral equations on periodic Lebesgue spaces

Journal of Mathematical Analysis and Applications

Volumn 348, Issue 2, 2008, Pages 775-786

  Lizama, Carlos ^a   Poblete, Verónica ^a  

^a UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

Author keywords

Additive perturbation; Fourier multipliers; Integral equations; Maximal regularity; Periodic solutions; R boundedness

Indexed keywords

EID: 51249091196     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.07.075     Document Type: Article

References (35)

1. Amann H. Linear parabolic equations with singular potentials. J. Evol. Equ. 3 (2003) 395-406
2. Amann H. On the strong solvability of the Navier-Stokes equations. J. Math. Fluid Mech. 2 (2000) 16-98
3. Amann H. Compact embeddings of vector-valued Sobolev and Besov spaces. Glas. Mat. Ser. III 35 1 (2000) 161-177
4. Amann H. Linear and Quasilinear Parabolic Problems. Monogr. Math. vol. 89 (1995), Birkhäuser Verlag, Basel
5. Arendt W. Semigroups and evolution equations: Functional calculus, regularity and kernel estimates. In: Dafermos C.M., and Feireisl E. (Eds). Handbook of Differential Equations, vol. 1, Evolutionary Equations (2004), Elsevier 1-85
6. Arendt W., Batty C.J.K., Hieber M., and Neubrander F. Vector-Valued Laplace Transforms and Cauchy Problems. Monogr. Math. vol. 96 (2001), Birkhäuser Verlag, Basel
7. Arendt W., Batty C., and Bu S. Fourier multipliers for Hölder continuous functions and maximal regularity. Studia Math. 160 (2004) 23-51
8. Arendt W., and Bu S. The operator-valued Marcinkiewicz multiplier theorem and maximal regularity. Math. Z. 240 (2002) 311-343
9. Berkson E., and Gillespie T.A. Spectral decompositions and harmonic analysis on UMD-spaces. Studia Math. 112 (1994) 13-49
10. 1 - BMO duality. Probability Theory and Harmonic Analysis (1986), Marcel Dekker, New York
11. Bu S., and Fang Y. Maximal regularity for integro-differential equation on periodic Triebel-Lizorkin spaces. Taiwanese J. Math. 12 2 (2008) 281-292
12. Bu S. Operator-valued Fourier multipliers and maximal regularity for vector-valued boundary problems. Adv. Math. (China) 34 1 (2005) 17-42 (in Chinese)
13. p-maximal regularity for second order Cauchy problems. Math. Z. 251 4 (2005) 751-781
14. Clément Ph., Londen S.O., and Simonett G. Quasilinear evolutionary equations and continuous interpolation spaces. J. Differential Equations 196 2 (2004) 418-447
15. Clément Ph., de Pagter B., Sukochev F.A., and Witvliet M. Schauder decomposition and multiplier theorems. Studia Math. 138 (2000) 135-163
16. Da Prato G., and Lunardi A. 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
17. Denk R., Hieber M., and Prüss J. R-boundedness, Fourier multipliers and problems of elliptic and parabolic type. Mem. Amer. Math. Soc. 166 788 (2003)
18. Escher J., Prüss J., and Simonett G. Analytic solutions for the Stefan problem with Gibbs-Thomson correction. J. Reine Angew. Math. 563 (2003) 1-52
19. Haase M. The Functional Calculus for Sectorial Operators. Oper. Theory Adv. Appl. vol. 169 (2006), Birkhäuser Verlag, Basel
20. ∞-calculus and sums of closed operators. Math. Ann. 321 (2001) 319-345
21. Keyantuo V., and Lizama C. Fourier multipliers and integro-differential equations in Banach spaces. J. London Math. Soc. (2) 69 (2004) 737-750
22. Keyantuo V., and Lizama C. Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces. Studia Math. 168 1 (2005) 25-50
23. V. Keyantuo, C. Lizama, V. Poblete, Periodic solutions of integro-differential equations in vector-valued function spaces, submitted for publication
24. p-regularity for parabolic equations, Fourier multiplier theorems and Hoo-functional calculus. In: Iannelli M., Nagel R., and Piazzera S. (Eds). Functional Analytic Methods for Evolution Equations. Lecture Notes in Math. vol. 1855 (2004), Springer 65-311
25. Lindenstrauss J., and Tzafriri L. Classical Banach Spaces II (1996), Springer, Berlin
26. Lizama C. Fourier multipliers and periodic solutions of delay equations in Banach spaces. J. Math. Anal. Appl. 324 2 (2006) 921-933
27. Martinez C., and Sanz M. The Theory of Fractional Powers of Operators. North-Holland Math. Stud. vol. 187 (2001), Elsevier, Amsterdam, London, New York
28. Monniaux S. On uniqueness for the Navier-Stokes system in 3D-bounded Lipschitz domains. J. Funct. Anal. 195 (2003) 1-11
29. Poblete V. Solutions of second order intergro-differential equations on periodic Besov spaces. Proc. Edinb. Math. Soc. (2) 50 (2007) 477-492
30. Portal P. Maximal regularity of evolution equations on discrete time scales. J. Math. Anal. Appl. 304 1 (2005) 1-12
31. Prüss J. Evolutionary Integral Equations and Applications. Monogr. Math. vol. 87 (1993), Birkhäuser Verlag
32. ′ = A K * u + B M * u. In: Favini A., Obrecht E., and Venni A. (Eds). Differential Equations in Banach Spaces (1986), Springer-Verlag, New York 227-242
33. Sobolevskii P.E. Fractional powers of coercively positive sums of operators. Soviet Math. Dokl. 16 (1975) 1638-1641
34. p-regularity. Math. Ann. 319 (2001) 735-758
35. p-regularity. Lect. Notes Pure Appl. Math. vol. 215 (2001), Marcel Dekker, New York 195-214