On boundedness of superposition operators in spaces of Triebel-Lizorkin type

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1. D. R. Adams, 10.1007/BF02385830, Ark. Mat. 14 (1976), 125-140. (1976) MR0417774DOI10.1007/BF02385830
2. G. Bourdaud, Sur les opérateurs peudo-différentiels à coefficients peu réguliers, Diss. Univ. de Paris-Sud, 1983. (1983) 
3. B. E. J. Dahlberg, A note on Sobolev spaces, Proc. Symp. Pure Math. 35, 1979, part I, 183-185. (1979) Zbl0421.46027MR0545257
4. D. E. Edmunds, H. Triebel, Remarks on nonlinear elliptic equations of the type $\Delta u+u={\left|u\right|}^p+f$ bounded domains, J. London Math. Soc. (2) 31 (1985), 331-339. (1985) MR0809954
5. C. Fefferman, E. M. Stein, 10.2307/2373450, Amer. J. Math. 93 (1971), 107-115. (1971) Zbl0222.26019MR0284802DOI10.2307/2373450
6. C. Fefferman, E. M. Stein, 10.1007/BF02392215, Acta Math. 129 (1972), 137-193. (1972) MR0447953DOI10.1007/BF02392215
7. M. Marcus, V. J. Mizel, 10.1007/BF00251378, Rational Mech. Anal. 42 (1972), 294-320. (1972) Zbl0236.46033MR0338765DOI10.1007/BF00251378
8. M. Marcus, V. J. Mizel, 10.1090/S0002-9947-1979-0531975-1, Trans. Amer. Math. Soc. 251 (1979), 187-218. (1979) MR0531975DOI10.1090/S0002-9947-1979-0531975-1
9. J. Marschall, Pseudo-differential operators with nonregular symbols, Thesis, FU Berlin (West), 1985. (1985) 
10. Y. Meyer, Remarques sur un théorème de J. M. Bony, Suppl. Rendiconti Circ. Mat. Palermo Serie II, 1 (1981), 1-20. (1981) Zbl0473.35021MR0639462
11. S. Mizohata, Lectures on the Cauchy problem, Tata Institute, Bombay 1965. (1965) MR0219881
12. J. Peetre, Interpolation of Lipschitz operators and metric spaces, Matematica (Cluj) 12 (35) (1970), 325-334. (1970) Zbl0217.44504MR0482280
13. J. Peetre, 10.1007/BF02386201, Ark. Mat. 13 (1975), 123-130. (1975) Zbl0302.46021MR0380394DOI10.1007/BF02386201
14. J. Rauch, An $L^2$-proof that $H^s$ is invariant under nonlinear maps for $s>\frac{n}{2}$, In: Global Analysis, Analysis on Manifolds, Teubner-Texte Math., 57, Teubner, Leipzig 1983. (1983) MR0730621
15. Th. Runst, 10.4171/ZAA/175, Z. Anal. Anwendungen 4 (1985), 557-573. (1985) Zbl0592.35011MR0818984DOI10.4171/ZAA/175
16. Th. Runst, 10.1007/BF01909369, Anal. Math. 12 (1986), 313-346. (1986) MR0877164DOI10.1007/BF01909369
17. W. Sickel, On pointwise multipliers in Besov-Triebel-Lizorkin spaces, Seminar Analysis 1986 (ed. by B.-W. Schulze and H. Triebel), Teubner-Texte Math., 96, Teubner, Leipzig 1987. (1986) MR0932288
18. W. Sickel, Superposition offunctions in spaces of Besov-Triebel-Lizorkin type. The critical case $1<s<\frac{n}{p}$, Seminar Analysis 1987 (ed. by B.-W. Schulze and H. Triebel), Teubner-Texte Math. 106, Teubner, Leipzig, 1988. (1987) MR1066752
19. G. Stampacchia, Equations elliptiques du second ordre à coefficients discontinues, Univ. Montreal Press, Quebec, 1966. (1966) MR0251373
20. E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton 1979. (1979) MR0290095
21. H. Triebel, Theory of function spaces, Akad. Verlagsges. Geest and Portig K. G., Leipzig and Birkhäuser Verlag, Basel, Boston, Stuttgart 1983. (1983) Zbl0546.46028MR0781540
22. H. Triebel, 10.1002/mana.3211170115, Math. Nachr. 117 (1984), 193-213. (1984) MR0755303DOI10.1002/mana.3211170115
23. M. Yamazaki, A quasi-homogeneous version of paradifferential operators I. Boundedness on spaces of Besov type, J. Fac. Sci. Univ. Tokyo, IA33 (1986), 131-174. (1986) Zbl0608.47058MR0837335
24. M. Yamazaki, A quasi-homogeneous version of the microlocal analysis for nonlinear partial differential equations, Preprint. Zbl0701.35162MR0977891

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