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Integrated semigroups and differential operators onL p spaces

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References

  • [A1] Arendt, W.: Vector valued Laplace transforms and Cauchy problems. Isr. J. Math.59, 327–352 (1987).

    Google Scholar 

  • [A2] Arendt, W.: Sobolev imbeddings and integrated semigroups. Preprint 1990

  • [A,K] Arendt, W., Kellermann, H.: Integrated solutions of Volterra integro-differential equations and applications. In: Da Prato, G., Iannelli, M. (eds.). Volterra integrodifferential equations in Banach spaces and applications. Proc. Conf. Trento 1987, 21–51, Pitman Res. Notes Math. Ser., 190. Harlow: Longman 1989

    Google Scholar 

  • [B, E] Balabane, M., Emamirad, H.A.:L p estimates for Schrödinger evolution equations. Trans. Am. Math. Soc.291, 357–373 (1985)

    Google Scholar 

  • [F, Stxxx] Fefferman, C., Stein, E.M.:H p spaces of several variables. Acta Math.129, 137–193 (1972).

    Google Scholar 

  • [G] Goldstein, J.A.: Semigroups of linear operators and applications. New York: Oxford University Press 1985

    Google Scholar 

  • [Hi1] Hieber, M.: Laplace transforms and α-times integrated semigroups. To appear in Forum Math.

  • [Hi2] Hieber, M.: Integrated semigroups and the Cauchy problem for systems inL p-spaces. to appear in J. Math. Anal. Appl.

  • [Hö1] Hörmander, L.: Estimates for translation invariant operators inL p spaces. Acta Math.104, 93–140 (1960)

    Google Scholar 

  • [Hö2] Hörmander, L.: The analysis of linear partial differential operators. I. Berlin Heidelberg New York: Springer 1984

    Google Scholar 

  • [K, Hi] Kellermann, H., Hieber, M.: Interated semigroups. J. Funct. Anal.84, 160–180 (1989)

    Google Scholar 

  • [La] Lanconelli, E.: Valutazioni inL p(ℝn) della soluzione del problema di Cauchy per l'equazione di Schrödinger. Boll. Un. Mat. Ital.4, 591–607 (1968)

    Google Scholar 

  • [Li] Littman, W.: The wave operator andL p-norms. J. Math. Mech.12, 55–68 (1963)

    Google Scholar 

  • [M1] Miyachi, A.: On some Fourier multipliers forH p(ℝn). J. Fac. Sci. Univ. Tokyo27, 157–179 (1980)

    Google Scholar 

  • [M2] Miyachi, A.: On some estimates for the wave equation inL p andH p. J. Fac. Sci. Univ. Tokyo27, 331–354 (1980)

    Google Scholar 

  • [M3] Miyachi, A.: On some singular Fourier multipliers. J. Fac. Sci. Univ. Tokyo28, 267–315 (1981)

    Google Scholar 

  • [N] Neubrander, F.: Integrated semigroups and their applications to the abstract Cauchy problem. Pacific J. Math.135, 111–155 (1988)

    Google Scholar 

  • [P] Peral, J.C.:L p estimates for the wave equation. J. Funct. Anal.36, 114–145 (1980)

    Google Scholar 

  • [Sj] Sjöstrand, S.: On the Riesz means of the solution of the Schrödinger equation. Ann. Scuola Norm. Sup. Pisa24, 331–348 (1970)

    Google Scholar 

  • [St] Stein, E.M.: Singular integrals and differentiability properties of functions. New Jersey: Princeton University Press 1970

    Google Scholar 

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  1. Mathematisches Institut der Universität, Auf der Morgenstelle 10, W-7400, Tübingen, Federal Republic of Germany

    Matthias Hieber

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  1. Matthias Hieber
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Hieber, M. Integrated semigroups and differential operators onL p spaces. Math. Ann. 291, 1–16 (1991). https://doi.org/10.1007/BF01445187

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