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Totally characteristic pseudo-differential operators in Besov-Lizorkin-Triebel spaces

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Abstract

A full symbolic calculus for totally characteristic pseudo-differential operators acting in general scales of function spaces with conormal asymptotics of several types will be developed. By using modified methods we will show that the results of S. Rempel and B.-W. Schulze for full asymptotics in Sobolev spaces can be generalized for Besov-Lizorkin-Triebel spaces, in particular, Hölder spaces, with other types of asymptotics.

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References

  1. Beals, R.:L pand Hölder estimates for pseudodifferential operators: sufficient conditions. Ann. Inst. Fourier29 (1979) no. 3 vii, 239–260.

    Google Scholar 

  2. Bourdaud, G.:L p-estimates for certain non-regular pseudodifferential operators. Comm. Part. Diff. Equ.7 (9) (1982), 1023–1033.

    Google Scholar 

  3. Coifman, R. R., Meyer, Y.: Au-dela des opérateurs pseudodifferentiels. Astérisque 57 (1978), 2–184.

    Google Scholar 

  4. Franke, J. Elliptische Randwertprobleme in Besov-Triebel-Lizorkin-Räumen. Dissertation A, Friedrich-Schiller- Universität Jena 1985.

    Google Scholar 

  5. Kondratév, V. A. (Кондрат\Qyев, В. А.): Краевые задачи для эллиптических уравнений в областях с коническими или (Boundary value problems for elliptic equations in domains with conical points). Труды Моск. мат. о-ва.16 (1967), 209–293. (Transactions Moscow Math. Soc. (1967), 227–313.

    Google Scholar 

  6. Lewis, J. E., Parenti, C.: Pseudodifferential operators of Mellin type. Comm. Part. Diff. Equ.8 (5) (1983), 477–544.

    Google Scholar 

  7. Maz'ja, V. G., Plamenevskij, B. A. (Мазья, В. Г., Пламеневский, Б. А.): Оценки вL p и в классах Гёльдера и прницип максимума Миранда-Агмона для решений зллиптических краевых задач в областях с особыми точками на границе (Estimates inL p and in Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular boundary points). Math. Nachr.81 (1978), 25–82.

    Google Scholar 

  8. Melrose, R.: Transformation of boundary problems. Acta Math.147 (1981), 149–236.

    Google Scholar 

  9. Päivärinta, L.: Pseudo-differential operators in Hardy-Triebel spaces. Z. Analysis Anwendungen2,3 (1983), 235–242.

    Google Scholar 

  10. Plamenevskij, B. A. (Лламенэвский, Ъ. А.): Алгебры псевдодиффенциальных операторов (Algebras of pseudodifferential operators). Наука, Мосва, 1986.

    Google Scholar 

  11. Rempel, S., Schulze, B.-W.: Complete Mellin and Green symbolic calculus in spaces with conormal asymptotics. Ann. Global Anal. Geom.4/2 (1986), 137–224.

    Google Scholar 

  12. Taibleson, M.: On the theory of Lipschitz spaces of distributions on Euclideann-space. I. J. Math. Mech.3 (1964), 407–478; II. J. Math. Mech.14 (1965), 821–839.

    Google Scholar 

  13. Triebel, H.: Interpolation theory, function spaces, differential operators. VEB Deutscher Verlag der Wissenschaften, Berlin, 1978, and North Holland Publ. Comp., Amsterdam, New York, Oxford, 1978.

    Google Scholar 

  14. Triebel, H.: Spaces of Besov-Hardy-Sobolev type. Teubner-Texte Math.15, Teubner, Leipzig, 1978.

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Communicated by B.-W. Schulze

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Baranowski, M. Totally characteristic pseudo-differential operators in Besov-Lizorkin-Triebel spaces. Ann Glob Anal Geom 7, 3–27 (1989). https://doi.org/10.1007/BF00137399

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