Embedding vector-valued Besov spaces into spaces of γ-radonifying operators

Mathematische Nachrichten

Volumn 281, Issue 2, 2008, Pages 238-252

  Kalton, Nigel ^a   Van Neerven, Jan ^b   Veraar, Mark ^b   Weis, Lutz ^c  

^a UNIVERSITY OF MISSOURI   (United States)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

radonifying operators; Type and cotype; Vector valued besov spaces

Indexed keywords

EID: 46049103501     PISSN: 0025584X     EISSN: 15222616     Source Type: Journal    
DOI: 10.1002/mana.200510598     Document Type: Article

References (22)

1. H. Amann, Operator-valued Fourier multipliers, vector-valued Besov spaces, and applications, Math. Nachr. 186, 5-56 (1997).
2. H. Amann, Compact embeddings of vector-valued Sobolev and Besov spaces, Glas. Mat. Ser. III 35 (55), No. 1, 161-177 (2000).
3. J. Bergh and J. Löfström, Interpolation Spaces. An Introduction (Springer-Verlag, Berlin, 1976).
4. q-estimates for parabolic boundary value problems with inhomogeneous data, Math. Z. 257, No. 1, 193-224 (2007).
5. J. Diestel, H. Jarchow, and A. Tonge, Absolutely Summing Operators, Cambridge Studies in Advanced Mathematics Vol. 43 (Cambridge University Press, Cambridge, 1995).
6. ∞-functional calculus and dilations, Bull. Math. Soc. France, to appear.
7. M. Girardi and L. Weis, Operator-valued Fourier multiplier theorems on Besov spaces, Math. Nachr. 251, 34-51 (2003).
8. J. Hoffmann-Jørgensen and G. Pisier, The law of large numbers and the central limit theorem in Banach spaces, Ann. Probab. 4, No. 4, 587-599 (1976).
9. C. Kaiser and L. Weis, Wavelet transforms for functions with values in UMD spaces, submitted for publication.
10. N. J. Kalton and L. Weis, Euclidean structures and their applications to spectral theory, in preparation.
11. ∞-functional calculus and square function estimates, in preparation.
12. B. Maurey, Type, cotype and K-convexity, in: Handbook of the Geometry of Banach Spaces, Vol. 2 (North-Holland, Amsterdam, 2003), pp. 1299-1332.
13. B. Maurey and G. Pisier, Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach, Studia Math. 58, No. 1, 45-90 (1976).
14. J. M. A. M. van Neerven, M. C. Veraar, and L. Weis, Conditions for stochastic integrability in UMD Banach spaces, in: Banach Spaces and their Applications in Analysis, Essue in honor of Nigel Kalton's 60th birthday, de Gruyter Proceedings in Mathematics (de Gruyter, Berlin, 2007), pp. 127-146.
15. J. M. A. M. van Neerven, M. C. Veraar, and L. Weis, Stochastic integration in UMD Banach spaces, Ann. Probab. 35, No. 4, 1438-1478 (2007).
16. J. M. A. M. van Neerven and L. Weis, Stochastic integration of functions with values in a Banach space, Studia Math. 166, No. 2, 131-170 (2005).
17. J. M. A. M. van Neerven and L. Weis, Weak limits and integrals of Gaussian covariances in Banach spaces, Probab. Math. Statist. 25, 33-52 (2005).
18. A. Pe?czyński and M. Wojciechowski, Molecular decompositions and embedding theorems for vector-valued Sobolev spaces with gradient norm, Studia Math. 107, No. 1, 61-100 (1993).
19. J. Rosiński and Z. Suchanecki, On the space of vector-valued functions integrable with respect to the white noise, Colloq. Math. 43, No. 1, 183-201 (1980).
20. H.-J. Schmeisser, Vector-valued Sobolev and Besov spaces, in: Seminar Analysis of the Karl-Weierstraß-Institute of Mathematics 1985/86 (Berlin, 1985/86), Teubner-Texte zur Mathematik Bd. 96 (Teubner, Leipzig, 1987), pp. 4-44.
21. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland Mathematical Library Vol. 18 (North-Holland Publishing Co., Amsterdam, 1978).
22. H. Triebel, Theory of Function Spaces, Monographs in Mathematics Vol. 78 (Birkhäuser, Basel, 1983).