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Volumn 246, Issue 3, 2009, Pages 1007-1037

Periodic solutions of integro-differential equations in vector-valued function spaces

Author keywords

Besov spaces; k regular sequence; Lebesgue Bochner spaces; M boundedness; Operator valued Fourier multiplier; R boundedness; Strong and mild well posedness; Triebel Lizorkin spaces; UMD spaces

Indexed keywords


EID: 55649103177     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2008.09.007     Document Type: Article
Times cited : (30)

References (40)
  • 1
    • 0013332276 scopus 로고
    • Linear and Quasilinear Parabolic Problems
    • Birkhäuser, Basel
    • Amann H. Linear and Quasilinear Parabolic Problems. Monogr. Math. vol. 89 (1995), Birkhäuser, Basel
    • (1995) Monogr. Math. , vol.89
    • Amann, H.1
  • 2
    • 0001871487 scopus 로고    scopus 로고
    • Operator-valued Fourier multipliers, vector-valued Besov spaces and applications
    • Amann H. Operator-valued Fourier multipliers, vector-valued Besov spaces and applications. Math. Nachr. 186 (1997) 5-56
    • (1997) Math. Nachr. , vol.186 , pp. 5-56
    • Amann, H.1
  • 4
    • 67649383116 scopus 로고    scopus 로고
    • Semigroups and evolution equations: Functional calculus, regularity and kernel estimates
    • Evolutionary Equations, vol. I, North-Holland, Amsterdam
    • Arendt W. Semigroups and evolution equations: Functional calculus, regularity and kernel estimates. Evolutionary Equations, vol. I. Handb. Differ. Equ. (2004), North-Holland, Amsterdam 1-85
    • (2004) Handb. Differ. Equ. , pp. 1-85
    • Arendt, W.1
  • 5
    • 2442662590 scopus 로고    scopus 로고
    • Operator-valued Fourier multiplier on periodic Besov spaces and applications
    • Arendt W., and Bu S. Operator-valued Fourier multiplier on periodic Besov spaces and applications. Proc. Edinb. Math. Soc. (2) 47 (2004) 15-33
    • (2004) Proc. Edinb. Math. Soc. (2) , vol.47 , pp. 15-33
    • Arendt, W.1    Bu, S.2
  • 6
    • 0036628277 scopus 로고    scopus 로고
    • The operator-valued Marcinkiewicz multiplier theorem and maximal regularity
    • Arendt W., and Bu S. The operator-valued Marcinkiewicz multiplier theorem and maximal regularity. Math. Z. 240 (2002) 311-343
    • (2002) Math. Z. , vol.240 , pp. 311-343
    • Arendt, W.1    Bu, S.2
  • 7
    • 33748758802 scopus 로고    scopus 로고
    • Semigroups for Delay Equations
    • A.K. Peters, Boston, MA
    • Bátkai A., and Piazzera S. Semigroups for Delay Equations. Res. Notes Math. vol. 10 (2005), A.K. Peters, Boston, MA
    • (2005) Res. Notes Math. , vol.10
    • Bátkai, A.1    Piazzera, S.2
  • 8
    • 0002072217 scopus 로고
    • Spectral decompositions and harmonic analysis on UMD-spaces
    • Berkson E., and Gillespie T.A. Spectral decompositions and harmonic analysis on UMD-spaces. Studia Math. 112 (1994) 13-49
    • (1994) Studia Math. , vol.112 , pp. 13-49
    • Berkson, E.1    Gillespie, T.A.2
  • 10
    • 51249097512 scopus 로고    scopus 로고
    • Maximal regularity for integro-differential equation on periodic Triebel-Lizorkin spaces
    • Bu S., and Fang Y. Maximal regularity for integro-differential equation on periodic Triebel-Lizorkin spaces. Taiwanese J. Math. 12 2 (2008) 281-292
    • (2008) Taiwanese J. Math. , vol.12 , Issue.2 , pp. 281-292
    • Bu, S.1    Fang, Y.2
  • 11
    • 43149106937 scopus 로고    scopus 로고
    • Periodic solutions for second order integro-differential equations with infinite delay in Banach spaces
    • Bu S., and Fang Y. Periodic solutions for second order integro-differential equations with infinite delay in Banach spaces. Studia Math. 184 2 (2008) 103-119
    • (2008) Studia Math. , vol.184 , Issue.2 , pp. 103-119
    • Bu, S.1    Fang, Y.2
  • 12
    • 27144553704 scopus 로고    scopus 로고
    • Operator-valued Fourier multipliers on periodic Triebel spaces
    • Bu S., and Kim J. Operator-valued Fourier multipliers on periodic Triebel spaces. Acta Math. Sin. (Engl. Ser.) 21 (2005) 1049-1056
    • (2005) Acta Math. Sin. (Engl. Ser.) , vol.21 , pp. 1049-1056
    • Bu, S.1    Kim, J.2
  • 13
    • 0009280706 scopus 로고
    • Martingales and Fourier analysis in Banach spaces
    • Probability and Analysis. Varenna, 1985, Springer-Verlag, Berlin
    • Burkholder D.L. Martingales and Fourier analysis in Banach spaces. Probability and Analysis. Varenna, 1985. Lecture Notes in Math. vol. 1206 (1986), Springer-Verlag, Berlin 61-108
    • (1986) Lecture Notes in Math. , vol.1206 , pp. 61-108
    • Burkholder, D.L.1
  • 14
    • 0003210113 scopus 로고
    • Semi-Groups of Operators and Approximation
    • Springer-Verlag
    • Butzer P.L., and Berens H. Semi-Groups of Operators and Approximation. Grundlehren Math. Wiss. vol. 145 (1967), Springer-Verlag
    • (1967) Grundlehren Math. Wiss. , vol.145
    • Butzer, P.L.1    Berens, H.2
  • 15
    • 27844477793 scopus 로고    scopus 로고
    • p-maximal regularity for second order Cauchy problems
    • p-maximal regularity for second order Cauchy problems. Math. Z. 251 (2005) 751-781
    • (2005) Math. Z. , vol.251 , pp. 751-781
    • Chill, R.1    Srivastava, S.2
  • 16
    • 3042586902 scopus 로고
    • Existence and regularity results for an integral equation with infinite delay in Banach space
    • Clément Ph., and Da Prato G. Existence and regularity results for an integral equation with infinite delay in Banach space. Integral Equations Operator Theory 11 (1988) 480-500
    • (1988) Integral Equations Operator Theory , vol.11 , pp. 480-500
    • Clément, Ph.1    Da Prato, G.2
  • 17
    • 0038323109 scopus 로고    scopus 로고
    • p-space
    • Evolution Equations and Their Applications in Physical and Life Sciences. Proceeding of the Bad Herrenalb Conference. Lumer G., and Weis L. (Eds). Germany, 1999, Marcel Dekker, New York, NY
    • p-space. In: Lumer G., and Weis L. (Eds). Evolution Equations and Their Applications in Physical and Life Sciences. Proceeding of the Bad Herrenalb Conference. Germany, 1999. Lect. Notes Pure Appl. Math. vol. 215 (2001), Marcel Dekker, New York, NY 67-87
    • (2001) Lect. Notes Pure Appl. Math. , vol.215 , pp. 67-87
    • Clément, Ph.1    Prüss, J.2
  • 19
    • 3042672654 scopus 로고
    • Periodic solutions for linear integrodifferential equations with infinite delay in Banach spaces
    • Da Prato G., and Lunardi A. Periodic solutions for linear integrodifferential equations with infinite delay in Banach spaces. Lecture Notes in Math. 1223 (1985) 49-60
    • (1985) Lecture Notes in Math. , vol.1223 , pp. 49-60
    • Da Prato, G.1    Lunardi, A.2
  • 20
    • 0242287337 scopus 로고    scopus 로고
    • R-boundedness, Fourier multipliers and problems of elliptic and parabolic type
    • 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)
    • (2003) Mem. Amer. Math. Soc. , vol.166 , Issue.788
    • Denk, R.1    Hieber, M.2    Prüss, J.3
  • 21
    • 0003259059 scopus 로고
    • Elliptic Partial Differential Equations of Second Order
    • Springer-Verlag
    • Gilbarg D., and Trudinger N.S. Elliptic Partial Differential Equations of Second Order. Grundlehren Math. Wiss. vol. 224 (1983), Springer-Verlag
    • (1983) Grundlehren Math. Wiss. , vol.224
    • Gilbarg, D.1    Trudinger, N.S.2
  • 22
    • 0037235531 scopus 로고    scopus 로고
    • Operator-valued Fourier multiplier theorems on Besov spaces
    • Girardi M., and Weis L. Operator-valued Fourier multiplier theorems on Besov spaces. Math. Nachr. 251 (2003) 34-51
    • (2003) Math. Nachr. , vol.251 , pp. 34-51
    • Girardi, M.1    Weis, L.2
  • 23
    • 28444447137 scopus 로고    scopus 로고
    • Criteria for R-boundedness of operator families
    • Evolution Equations, Dekker, New York
    • Girardi M., and Weis L. Criteria for R-boundedness of operator families. Evolution Equations. Lect. Notes Pure Appl. Math. vol. 234 (2003), Dekker, New York 203-221
    • (2003) Lect. Notes Pure Appl. Math. , vol.234 , pp. 203-221
    • Girardi, M.1    Weis, L.2
  • 24
    • 0003359314 scopus 로고
    • Volterra Integral and Functional Equations
    • Cambridge Univ. Press, Cambridge, New York
    • Gripenberg G., Londen S.-O., and Staffans O. Volterra Integral and Functional Equations. Encyclopedia Math. Appl. vol. 34 (1990), Cambridge Univ. Press, Cambridge, New York
    • (1990) Encyclopedia Math. Appl. , vol.34
    • Gripenberg, G.1    Londen, S.-O.2    Staffans, O.3
  • 25
    • 20844433105 scopus 로고    scopus 로고
    • Convolutions, multipliers and maximal regularity on vector-valued Hardy spaces
    • Hytönen T. Convolutions, multipliers and maximal regularity on vector-valued Hardy spaces. J. Evol. Equ. 5 (2005) 205-225
    • (2005) J. Evol. Equ. , vol.5 , pp. 205-225
    • Hytönen, T.1
  • 26
    • 55649119219 scopus 로고    scopus 로고
    • Mild well-posedness of abstract differential equations
    • Amann H., Arendt W., Hieber M., Neubrander F., Nicaise S., and von Below J. (Eds), Birkhäuser, Basel
    • Keyantuo V., and Lizama C. Mild well-posedness of abstract differential equations. In: Amann H., Arendt W., Hieber M., Neubrander F., Nicaise S., and von Below J. (Eds). Functional Analysis and Evolution Equations (2008), Birkhäuser, Basel 371-387
    • (2008) Functional Analysis and Evolution Equations , pp. 371-387
    • Keyantuo, V.1    Lizama, C.2
  • 27
    • 33748592817 scopus 로고    scopus 로고
    • Hölder continuous solutions for integro-differential equations and maximal regularity
    • Keyantuo V., and Lizama C. Hölder continuous solutions for integro-differential equations and maximal regularity. J. Differential Equations 230 (2006) 634-660
    • (2006) J. Differential Equations , vol.230 , pp. 634-660
    • Keyantuo, V.1    Lizama, C.2
  • 28
    • 17044384229 scopus 로고    scopus 로고
    • Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces
    • 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) 25-49
    • (2005) Studia Math. , vol.168 , Issue.1 , pp. 25-49
    • Keyantuo, V.1    Lizama, C.2
  • 29
    • 3042637814 scopus 로고    scopus 로고
    • Fourier multipliers and integro-differential equations in Banach spaces
    • Keyantuo V., and Lizama C. Fourier multipliers and integro-differential equations in Banach spaces. J. London Math. Soc. 69 3 (2004) 737-750
    • (2004) J. London Math. Soc. , vol.69 , Issue.3 , pp. 737-750
    • Keyantuo, V.1    Lizama, C.2
  • 30
    • 17044413547 scopus 로고    scopus 로고
    • ∞-functional calculus
    • Functional Analytic Methods for Evolution Equations. Iannelli M., Nagel R., and Piazzera S. (Eds), Springer-Verlag
    • ∞-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-Verlag 65-311
    • (2004) Lecture Notes in Math. , vol.1855 , pp. 65-311
    • Kunstmann, P.1    Weis, L.2
  • 31
    • 55049107032 scopus 로고    scopus 로고
    • Maximal regularity of second-order equations with delay
    • Poblete V. Maximal regularity of second-order equations with delay. J. Differential Equations 246 1 (2009) 261-276
    • (2009) J. Differential Equations , vol.246 , Issue.1 , pp. 261-276
    • Poblete, V.1
  • 32
    • 0003334487 scopus 로고
    • Evolutionary Integral Equations and Applications
    • Birkhäuser, Basel
    • Prüss J. Evolutionary Integral Equations and Applications. Monogr. Math. vol. 87 (1993), Birkhäuser, Basel
    • (1993) Monogr. Math. , vol.87
    • Prüss, J.1
  • 33
    • 0039798218 scopus 로고
    • Some Banach space techniques in vector-valued Fourier analysis
    • Rubio de Francia J.L., and Torrea J.L. Some Banach space techniques in vector-valued Fourier analysis. Colloq. Math. 54 (1987) 273-284
    • (1987) Colloq. Math. , vol.54 , pp. 273-284
    • Rubio de Francia, J.L.1    Torrea, J.L.2
  • 35
    • 0242463498 scopus 로고
    • Existence in the large for a semilinear integrodifferential equation with infinite delay
    • Sforza D. Existence in the large for a semilinear integrodifferential equation with infinite delay. J. Differential Equations 120 (1995) 289-303
    • (1995) J. Differential Equations , vol.120 , pp. 289-303
    • Sforza, D.1
  • 36
    • 55649107577 scopus 로고
    • 2-solutions of an integrodifferential equation in Hilbert space
    • 2-solutions of an integrodifferential equation in Hilbert space. Proc. Amer. Math. Soc. 117 3 (1993) 745-751
    • (1993) Proc. Amer. Math. Soc. , vol.117 , Issue.3 , pp. 745-751
    • Staffans, O.J.1
  • 37
    • 55649111214 scopus 로고
    • Fractals and Spectra. Related to Fourier Analysis and Function Spaces
    • Birkhäuser, Basel
    • Triebel H. Fractals and Spectra. Related to Fourier Analysis and Function Spaces. Monogr. Math. vol. 78 (1983), Birkhäuser, Basel
    • (1983) Monogr. Math. , vol.78
    • Triebel, H.1
  • 38
    • 0003295738 scopus 로고    scopus 로고
    • Theory of Function Spaces
    • Birkhäuser, Basel
    • Triebel H. Theory of Function Spaces. Monogr. Math. vol. 91 (1997), Birkhäuser, Basel
    • (1997) Monogr. Math. , vol.91
    • Triebel, H.1
  • 39
    • 0035629005 scopus 로고    scopus 로고
    • p-regularity
    • p-regularity. Math. Ann. 319 (2001) 735-758
    • (2001) Math. Ann. , vol.319 , pp. 735-758
    • Weis, L.1
  • 40
    • 0000324741 scopus 로고
    • On vector-valued Fourier multiplier theorems
    • Zimmermann F. On vector-valued Fourier multiplier theorems. Studia Math. 93 (1989) 201-222
    • (1989) Studia Math. , vol.93 , pp. 201-222
    • Zimmermann, F.1


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