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Examples of pseudo-differential operators inL p spaces with unbounded imaginary powers

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References

  1. H.Amann, Linear and Quasilinear Parabolic Problems. Basel 1995.

  2. H. Amann, M. Hieber andG. Simonett, BoundedH -calculus for elliptic operators. Differential Integral Equations7, 613–653 (1994).

    Google Scholar 

  3. J. B. Baillon andP. Clément, Examples of unbounded imaginary powers of operators. J. Funct. Anal.100, 419–434 (1991).

    Google Scholar 

  4. M.Cowling, I.Doust, A.Mcintosh and A.Yagi, Banach space operators with a boundedH functional calculus. Preprint 1993.

  5. G. Dore andA. Venni, On the closedness of the sum of two closed operators. Math. Z.196, 189–201 (1987).

    Google Scholar 

  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. Y. Giga, Domains of fractional powers of the Stokes operator inL r spaces. Arch. Rational Mech. Anal.89, 251–265 (1985).

    Google Scholar 

  9. M. Hieber, Integrated semigroups and differential operators onL p spaces. Math. Ann.291, 1–16 (1991).

    Google Scholar 

  10. M.Hieber, Heat kernel estimates and boundedH -calculus onL p spaces. In: Partial Differential Equations; Models in Physics and Biology, S. Nicaise, G. Lumer, B.-W. Schulze, eds., 166–173, Berlin 1994.

  11. M.Hieber and J.Prüss, Functional calculi for linear operators in vector-valuedL p spaces via the Transference-Principle. Submitted.

  12. L. Hörmander, Estimates for translation invariant operators inL p spaces. Acta Math.104, 93–140 (1960).

    Google Scholar 

  13. H. Komatsu, Fractional powers of operators. Pacific J. Math.9, 285–346 (1966).

    Google Scholar 

  14. V. Lebedev andA. Olevskii,C 1 Change of variable: Beuerling-Helson type theorem and Hörmander conjecture on Fourier multipliers. Geom. Funct. Anal.4, 213–235 (1994).

    Google Scholar 

  15. A. Miyachi, On some singular Fourier multipliers. J. Fac. Sci. Univ. Tokyo28, 267–315 (1981).

    Google Scholar 

  16. A. McIntosh andA. Yagi, Operators of type ω without a boundedH -functional calculus. In: Miniconference on Operators in Analysis, 1989. Proceedings of the Centre for Math. Analysis, ANU, Canberra,24, 159–172 (1990).

    Google Scholar 

  17. J.Prüss, Evolutionary Integral Equations and Applications. Basel 1993.

  18. J. Prüss andH. Sohr, On operators with bounded imaginary powers in Banach spaces. Math. Z.203, 429–452 (1990).

    Google Scholar 

  19. J. Prüss andH. Sohr, Imaginary powers of elliptic second order differential operators inL p-spaces. Hiroshima Math. J.23, 161–192 (1993).

    Google Scholar 

  20. R. T. Seeley, The resolvent of an elliptic boundary value problem. Amer. J. Math.91, 889–920 (1969).

    Google Scholar 

  21. A.Venni, A counterexample concerning imaginary powers of linear operators. In: Functional Analysis and Related Topics, 1991, H. Komatsu, ed., LNM1540, Berlin-Heidelberg-New York 1993.

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Hieber, M. Examples of pseudo-differential operators inL p spaces with unbounded imaginary powers. Arch. Math 66, 126–131 (1996). https://doi.org/10.1007/BF01273343

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