Convolutions, multipliers and maximal regularity on vector-valued Hardy spaces

Journal of Evolution Equations

Volumn 5, Issue 2, 2005, Pages 205-225

  Hytönen, Tuomas P ^a,b  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b AALTO UNIVERSITY   (Finland)

Author keywords

Abstract Cauchy problem; Hardy spaces of vector valued functions; Maximal regularity; Operator valued Fourier multipliers

Indexed keywords

EID: 20844433105     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00028-005-0184-0     Document Type: Article

References (25)

1. ARENDT, W. and BU, S. The operator-valued Marcinkiewicz multiplier theorem and maximal regularity. Math. Z. 240 (2002), 311-343.
2. BENEDEK, A., CALDERÓN, A. P. and PANZONE, R., Convolution operators on Banach space valued functions. Proc. Nat. Acad. Sci. USA 48 (1962), 356-365.
3. BLASCO, O., Hardy spaces of vector-valued functions: duality. Trans. Amer. Math. Soc. 308 (1988), 495-507.
4. CHUESHOV, I. and LASIECKA, I., Inertial manifolds for von Kármán plate equations. Appl. Math. Optim. 46 (2002), 179-206.
5. CLÉMENT, PH., LONDEN, S.-O. and SIMONETT, G., Quasilinear evolutionary equations and continuous interpolation spaces. J. Differential Equations 196(2) (2004), 418-447.
6. CLÉMENT, PH., DE PAGTER, B., SUKOCHEV, F. A. and WITVLIET, H. Schauder decompositions and multiplier theorems. Studia Math. 138 (2000), 135-163.
7. p-spaces. In: G. Lumer, L. Weis (eds.), Evolution Equations and Their Applications in Physical and Life Sciences, Marcel Dekker (2000), 67-78.
8. 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).
9. p-regularity for abstract differential equations. In: H. Komatsu (ed.), Functional Analysis and Related Topics, Lecture Notes in Math. 1540, Springer (1993), 25-38.
10. p spaces for an abstract Cauchy problem. Adv. Differ. Equ. 5 (2000), 293-322.
11. ENGEL, K.-J. and NAGEL, R. One-Parameter Semigroups for Linear Evolution Equations. Graduate Texts in Math. 194, Springer-Verlag, New York-Berlin-Heidelberg, 2000.
12. GARCÍA-CUERVA, J. and RUBIO DE FRANCIA, J. L. Weighted Norm Inequalities and Related Topics. North-Holland Math. Studies 116, North Holland, Amsterdam, 1985.
13. p(X) and geometry of Banach spaces. J. Funct. Anal. 204(2) (2003), 320-354.
14. HYTÖNEN, T., Translation-invariant operators on spaces of vector-valued functions. Doctoral dissertation, Helsinki University of Technology, 2003. Available at http://lib.hut.fi/Diss/2003/isbn9512264579/.
15. HYTÖNEN, T. and WEIS, L., Singular convolution integrals with operator-valued kernel. Math. Z., to appear.
16. p-maximal regularity. Math. Z. 235 (2000), 559-568.
17. KURTZ, D. S. and WHEEDEN, R. L., Results on weighted norm inequalities for multipliers. Trans. Amer. Math. Soc. 255 (1979), 343-362.
18. RUBIO DE FRANCIA, J. L., Martingale and integral transforms of Banach space valued functions. In: Probability in Banach spaces, Lecture Notes in Math. 1221, 195-222. Springer, 1986.
19. SOBOLEVSKIǏ, P. E. Coerciveness inequalities for abstract parabolic equations. Soviet Math. Dokl. 5(4) (1964), 894-897.
20. (Translation from Dokl. Akad. Nauk SSSR 157 (1964), 52-57, by R. N. Goss)
21. STEIN, E. M., Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton Math. Series 43. Princeton Univ. Press, NJ, 1993.
22. ŠTRKALJ, Ž. and WEIS, L. On operator-valued multiplier theorems. Trans. Amer. Math. Soc., to appear.
23. STRÖMBERG, J.-O. and TORCHINSKY, A. Weighted Hardy Spaces. Lecture Notes in Math. 1381. Springer, 1989.
24. p-regularity. Math. Ann. 319 (2001), 735-758.
25. ZYGMUND, A. Trigonometric Series, Vol. II. Cambridge Univ. Press, 1979.