Maximal regularity of second order delay equations in Banach spaces

Science China Mathematics

Volumn 53, Issue 1, 2010, Pages 51-62

  Bu, Shang Quan ^a   Fang, Yi ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Besov spaces; Lebesgue Bochner spaces; Maximal regularity; Second order delay equations; Triebel Lizorkin spaces

Indexed keywords

EID: 77649216163     PISSN: 16747283     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11425-009-0108-5     Document Type: Article

References (16)

1. Arendt W, Bu S. The operator-valued Marcinkiewicz multiplier theorems and maximal regularity. Math Z, (2002) 240: 311-343.
2. Arendt W, Bu S. Operator-valued Fourier multipliers on periodic Besov spaces and applications. Proc Edinb Math Soc, 2004, 47: 15-33.
3. Bátkai A, Fašanga E, Shvidkoy R. Hyperbolicity of delay equations via Fourier multipliers. Acta Sci Math (Szeged), 2003, 69: 131-145.
4. 1-BMO duality. In: Probability Theory and Harmonic Analysis. Festbooks Pure Appl Math, 98. New York: Dekker, 1988, 1-19.
5. Bu S. Maximal regularity of second order delay equations in Banach spaces. Acta Math Sin (Engl Ser), 2009, 25: 21-28.
6. Bu S, Fang Y. Periodic solutions for second order integro-differential equations with infinite delay in Banach spaces. Studia Math, 2008, 184: 103-119.
7. Bu S, Kim J. Operator-valued Fourier multipliers on periodic Triebel spaces. Acta Math Sin (Engl Ser), 2004, 21: 1049-1056.
8. Hale J K. Theory of Functional Differential Equations. Appl Math Sci, New York: Springer-Verlag, 1977.
9. Keyantuo V, Lizama C. Periodic solutions of second order differential equations in Banach spaces. Math Z, 2006, 253: 489-514.
10. Latushkin Y, Räbiger F. Operator valued Fourier multipliers and stability of strongly continuous semigroups. Integral Equations Operator Theory, 2005, 51: 375-394.
11. Lindenstrauss J, Tzafriri L. Classical Banach Spaces II. Berlin: Springer-Verlag, 1979.
12. Lizama C. Fourier multipliers and periodic solutions of delay equations in Banach spaces. J Math Anal Appl, 2006, 324: 921-933.
13. Lizama C, Poblete V. Maximal regularity of delay equations in Banach spaces. Studia Math, 2006, 175: 91-102.
14. p-spaces. J Differential Equations, 1976, 29: 71-89.
15. p-regularity. Math Ann, 2001, 319: 735-758.
16. p-regularity. In: Evolution Equations and Their Applications in Physical and Life Sciences. Lecture Notes in Pure and Appl Math, 215. New York: Dekker, 2001, 195-214.