Examples of pseudo-differential operators in Lp spaces with unbounded imaginary powers

Archiv der Mathematik

Volumn 66, Issue 2, 1996, Pages 126-131

  Hieber, Matthias ^a  

^a UNIVERSITY OF ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030306828     PISSN: 0003889X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01273343     Document Type: Article

References (21)

1. H. AMANN, Linear and Quasilinear Parabolic Problems. Basel 1995.
2. ∞-calculus for elliptic operators. Differential Integral Equations 7, 613-653 (1994).
3. J. B. BAILLON and P. CLÉMENT, Examples of unbounded imaginary powers of operators. J. Funct. Anal. 100, 419-434 (1991).
4. ∞ functional calculus. Preprint 1993.
5. G. DORE and A. VENNI, On the closedness of the sum of two closed operators. Math. Z. 196, 189-201 (1987).
6. X. T. DUONG and D. W. ROBINSON, Semigroup kernels, Poisson bounds and holomorphic functional calculus. Research Report, CMA, Australien National University 1995.
7. R. E. EDWARDS and G. I. GAUDRY, Littlewood-Paley and Multiplier theory. Berlin-Heidelberg-New York 1977.
8. r spaces. Arch. Rational Mech. Anal. 89, 251-265 (1985).
9. p spaces. Math. Ann. 291, 1-16 (1991).
10. p spaces. In: Partial Differential Equations; Models in Physics and Biology, S. Nicaise, G. Lumer, B.-W. Schulze, eds., 166-173, Berlin 1994.
11. p spaces via the Transference-Principle. Submitted.
12. p spaces. Acta Math. 104, 93-140 (1960).
13. H. KOMATSU, Fractional powers of operators. Pacific J. Math. 9, 285-346 (1966).
14. 1 Change of variable: Beuerling-Helson type theorem and Hörmander conjecture on Fourier multipliers. Geom. Funct. Anal. 4, 213-235 (1994)
15. A. MIYACHI, On some singular Fourier multipliers. J. Fac. Sci. Univ. Tokyo 28, 267-315 (1981).
16. A. MCINTOSH and A. YAGI, Operators of type ω without a bounded H∞-functional calculus. In: Miniconference on Operators in Analysis, 1989. Proceedings of the Centre for Math. Analysis, ANU, Canberra, 24, 159-172 (1990).
17. J. PRÜSS, Evolutionary Integral Equations and Applications. Basel 1993.
18. J. PRÜSS and H. SOHR, On operators with bounded imaginary powers in Banach spaces. Math. Z. 203, 429-452 (1990).
19. p-spaces. Hiroshima Math. J. 23, 161-192 (1993).
20. R. T. SEELEY, The resolvent of an elliptic boundary value problem. Amer. J. Math. 91, 889-920 (1969).
21. A. VENNI, A counterexample concerning imaginary powers of linear operators. In: Functional Analysis and Related Topics, 1991, H. KOMATSU, ed., LNM 1540, Berlin-Heidelberg-New York 1993.