Two-sided eigenvalue estimates for subordinate processes in domains

Journal of Functional Analysis

Volumn 226, Issue 1, 2005, Pages 90-113

  Chen, Zhen Qing ^a   Song, Renming ^b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Bernstein function; Borel right process; Brownian motion; Complete Bernstein function; Dirichlet form; Eigenvalues; L vy process; Resolvent; Semigroup; Spherically symmetric stable process; Subordination; Subordinator

Indexed keywords

EID: 23344440772     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2005.05.004     Document Type: Article

References (33)

1. R. Bañuelos T. Kulczycki The Cauchy process and the Steklov problem J. Funct. Anal. 211 2004 355-423
2. R. Bañuelos R. Latała P.J. Mendez-Hernandez A Brascamp-Lieb-Luttinger-type inequality and applications to symmetric stable processes Proc. Amer. Math. Soc. 129 2001 2997-3008
3. J. Bertoin Lévy Processes 1996 Cambridge University Press Cambridge
4. D. Betsakos, Symmetrization, symmetric stable processes, and Riesz capacities, Trans. Amer. Math. Soc. 356 (2004) 735-755, with an addendum in Trans. Amer. Math. Soc. 356 (2004) 3821.
5. R.M. Blumenthal R.K. Getoor The asymptotic distribution of the eigenvalues for a class of Markov operators Pacific J. Math. 9 1959 399-408
6. K. Bogdan The boundary Harnack principle for the fractional Laplacian Studia Math. 123 1997 43-80
7. K. Bogdan Representation of α-harmonic functions in Lipschitz domains Hiroshima Math. J. 29 1999 227-243
8. K. Bogdan T. Byczkowski Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains Studia Math. 133 1999 53-92
9. I. Chavel Eigenvalues in Riemannian Geometry 1984 Academic Press New York
10. Z.-Q. Chen Multidimensional symmetric stable processes Korean J. Comput. Appl. Math. 6 1999 227-266
11. Z.-Q. Chen R. Song Intrinsic ultracontractivity and conditional gauge for symmetric stable processes J. Funct. Anal. 150 1997 204-239
12. Z.-Q. Chen R. Song Estimates on Green functions and Poisson kernels for symmetric stable processes Math. Ann. 312 1998 465-501
13. Z.-Q. Chen R. Song Martin boundary and integral representation for harmonic functions of symmetric stable processes J. Funct. Anal. 159 1998 267-294
14. Z.-Q. Chen R. Song Intrinsic ultracontractivity, conditional lifetimes and conditional gauge for symmetric stable processes on rough domains Illinois J. Math. 44 2000 138-160
15. Z.-Q. Chen R. Song Drift transforms and Green function estimates for discontinuous processes J. Funct. Anal. 201 2003 262-281
16. E.B. Davies One-Parameter Semigroups 1980 Academic Press London
17. E.B. Davies Heat Kernels and Spectral Theory 1989 Cambridge University Press Cambridge
18. R.D. DeBlassie Higher order PDEs and symmetric stable processes Probab. Theory Related Fields 129 2004 495-536
19. R.D. DeBlassie, Correction to Higher order PDEs and symmetric stable processes, Preprint.
20. M. Fukushima Y. Oshima M. Takeda Dirichlet Forms and Symmetric Markov Processes 1994 Walter De Gruyter Berlin
21. N. Jacob, Pseudo Differential Operators and Markov Processes, vol. 1, Imperial College Press, London, 2001.
22. L.B. Klebanov G.M. Maniya I.A. Melamed A problem of V.M. Zolotarev and analogues of infinitely divisible and stable distributions in a scheme for summation of a random number of random variables Theory Probab. Appl. 29 1984 791-794
23. T. Kulczycki Properties of Green function of symmetric stable processes Probab. Math. Statist. 17 1997 339-364
24. T. Kulczycki Intrinsic ultracontractivity for symmetric stable processes Bull. Polish Acad. Sci. Math. 46 1998 325-334
25. P.J. Mendez-Hernandez Brascamp-Lieb-Luttinger inequalities for convex domains of finite inradius Duke Math. J. 113 2002 93-131
26. Y. Nakamura, Classes of operator monotone functions and Stieltjes functions, in: H. Dym et al. (Eds.), The Gohberg Anniversary Collection, vol. II: Topics in Analysis and Operator Theory, Operator Theory: Advances and Applications, vol. 41, Birkhäuser, Basel, 1989, pp. 395-404.
27. H. Okura Recurrence and transience criteria for subordinated symmetric Markov processes Forum Math. 14 2002 121-146
28. M. Reed, B. Simon, Methods of Modern Mathematical Physics, vol. 4, Analysis of Operators, Academic Press, New York, 1978.
29. M. Ryznar Estimates of Green function for relativistic α-stable process Potential Anal. 17 2002 1-23
30. R.L. Schilling, On the domain of the generator of a subordinate semigroup, Potential Theory-ICPT 94 (Kouty, 1994), de Gruyter, Berlin, 1996, pp. 449-462.
31. H. Sikić, R. Song, Z. Vondraček, Potential theory of geometric stable processes, Preprint, 2004.
32. R. Song Z. Vondracek Potential theory of subordinate killed Brownian motion in a domain Probab. Theory Related Fields 135 2003 578-592
33. R. Song J.-M. Wu Boundary Harnack principle for symmetric stable processes J. Funct. Anal. 168 1999 403-427