Function spaces as dirichlet spaces (about a paper by Maz'ya and Nagel)

Zeitschrift für Analysis und ihre Anwendungen

Volumn 24, Issue 1, 2005, Pages 3-28

  Jacob, Niels ^a   Schilling, René L ^b  

^a SWANSEA UNIVERSITY   (United Kingdom)

^b PHILIPPS UNIVERSITY MARBURG   (Germany)

Author keywords

Anisotropic Sobolev space; Bernstein function; Dirichlet space; Negative definite function; Slobodeckij norm

Indexed keywords

EID: 20444483578     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/ZAA/1228     Document Type: Article

References (25)

1. Alzer, H. and C. Berg: Some classes of completely monotonic functions. Ann. Acad. Sci. Fenn. 27 (2002), 445-460.
2. Andrews, G. E., Askey, R. and R. Roy: Special Functions. Encycl. Math. Appl. Vol. 71. Cambridge: Cambridge University Press 1999.
3. Berg, C.: Integral representation of some functions related to the Gamma function. Mediterranean J. Math., to appear.
4. Berg, C. and G. Forst: Potential Theory on Locally Compact Abelian Groups. Ergeb. Math. Grenzgeb. Bd. 87. Berlin: Springer-Verlag 1975.
5. Berg, C. and H. L. Pedersen: A completely monotone function related to the Gamma function. J. Comp. Appl. Math. 133 (2001), 219-230.
6. Beurling, A. and J. Deny: Dirichlet Spaces. Proc. Natl. Acad. Sci. U.S.A. 45 (1959), 208-215.
7. Farkas, W. and H.-G. Leopold: Characterisations of function spaces of generalised smoothness. Ann. Mat. Pura Appl., to appear.
8. Harzallah, Kh.: Fonctions opérant sur les fonctions définies-négatives. Ann. Inst. Fourier 17 (1967)(1), 443-468.
9. Hörmander, L.: Linear Partial Differential Operators. Grundlehren Math. Wiss. Bd. 116. Berlin: Springer-Verlag 1963.
10. Hörmander, L.: The Analysis of Linear Partial Differential Operators II. Grundlehren Math. Wiss. Bd. 257. Berlin: Springer-Verlag 1983.
11. Ismail, M. E. H.: Bessel functions and the infinite divisibility of the Student t-distribution. Ann. Probab. 5 (1977), 582-585.
12. Ismail, M. E. H., Integral representations an complete monotonicity of various quotients of Bessel functions. Can. J. Math. 29 (1977), 1198-1207.
13. Ismail, M. E. H. and C. Ping May: Special functions, infinite divisibility and transcendental equations. Math. Proc. Camb. Phil. Soc. 85 (1979), 453-464.
14. Ismail, M. E. H.: Complete monotonicity of modified Bessel functions. Proc. Am. Math. Soc. 108 (1990), 353-361.
15. Ismail, M. E. H. and K. S. Miller: An infinitely divisible distribution involving modified Bessel functions. Proc. Am. Math. Soc. 85 (1982), 233-238.
16. Jacob, N.: Pseudo Differential Operators and Markov Processes. Vol. 1: Fourier Analysis and Semigroups. London: Imperial College Press 2001.
17. Kahane, J.-P.: Sur les fonctions de type positif et de type négatif. In: Seminar on Harmonic Analysis 1978-79. Publ. Math. Orsay 79.7, Univ. Paris XI, Orsay 1979, pp. 21-37.
18. n). Beitr. Anal. 12 (1978), 7-17.
19. Nagel, J.: Äquivalente Normierungen in Funktionalräumen (in Russian). Vestn. L.G.U. 7 (1974), 41-47.
20. Nagel, J.: Verallgemeinerte Slobodezki-Räume auf der Halbachse. Beitr. Anal. 15 (1981), 61-70.
21. Schilling, R. L.: Zum Pfadverhalten von Markovschen Prozessen, die mit Lévy-Prozessen vergleichbar sind. Dissertation, Universität Erlangen 1994.
22. Schilling, R. L.: Subordination in the sense of Bochner and a related functional calculus. J. Aust. Math. Soc. Ser. A 64 (1998), 368-396.
23. Schoenberg, I. J.: Metric spaces and completely monotone functions. Ann. Math. 39 (1938), 811-842.
24. Song, R.: Private Communication, September 2004.
25. Triebel, H.: The Structure of Functions. Monogr. Math. Vol. 97. Basel: Birkhäuser Verlag 2001.