On boundedness of superposition operators in spaces of Triebel-Lizorkin type
Czechoslovak Mathematical Journal, Tome 39 (1989) no. 2, pp. 323-347
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

DOI : 10.21136/CMJ.1989.102305
Classification : 46E35, 47H99
@article{10_21136_CMJ_1989_102305,
     author = {Sickel, Winfried},
     title = {On boundedness of superposition operators in spaces of {Triebel-Lizorkin} type},
     journal = {Czechoslovak Mathematical Journal},
     pages = {323--347},
     year = {1989},
     volume = {39},
     number = {2},
     doi = {10.21136/CMJ.1989.102305},
     mrnumber = {992137},
     zbl = {0693.46039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1989.102305/}
}
TY  - JOUR
AU  - Sickel, Winfried
TI  - On boundedness of superposition operators in spaces of Triebel-Lizorkin type
JO  - Czechoslovak Mathematical Journal
PY  - 1989
SP  - 323
EP  - 347
VL  - 39
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1989.102305/
DO  - 10.21136/CMJ.1989.102305
LA  - en
ID  - 10_21136_CMJ_1989_102305
ER  - 
%0 Journal Article
%A Sickel, Winfried
%T On boundedness of superposition operators in spaces of Triebel-Lizorkin type
%J Czechoslovak Mathematical Journal
%D 1989
%P 323-347
%V 39
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1989.102305/
%R 10.21136/CMJ.1989.102305
%G en
%F 10_21136_CMJ_1989_102305
Sickel, Winfried. On boundedness of superposition operators in spaces of Triebel-Lizorkin type. Czechoslovak Mathematical Journal, Tome 39 (1989) no. 2, pp. 323-347. doi: 10.21136/CMJ.1989.102305

[1] D. R. Adams: Qn the existence of capacitary strong type estimates in $R_n$. Ark. Mat. 14 (1976), 125-140. | DOI | MR

[2] G. Bourdaud: Sur les opérateurs peudo-différentiels à coefficients peu réguliers. Diss. Univ. de Paris-Sud, 1983.

[3] B. E. J. Dahlberg: A note on Sobolev spaces. Proc. Symp. Pure Math. 35, 1979, part I, 183-185. | MR | Zbl

[4] D. E. Edmunds, H. Triebel: Remarks on nonlinear elliptic equations of the type $\Delta u + u = |u|^p + f$ bounded domains. J. London Math. Soc. (2) 31 (1985), 331-339. | MR

[5] C. Fefferman, E. M. Stein: Some maximal inequalities. Amer. J. Math. 93 (1971), 107-115. | DOI | MR | Zbl

[6] C. Fefferman, E. M. Stein: $H^p$ spaces of several variables. Acta Math. 129 (1972), 137-193. | DOI | MR

[7] M. Marcus, V. J. Mizel: Absolute continuity on tracks and mappings of Sobolev spaces. Rational Mech. Anal. 42 (1972), 294-320. | DOI | MR | Zbl

[8] M. Marcus, V. J. Mizel: Complete characterizations of functions which act via superposition on Sobolev spaces. Trans. Amer. Math. Soc. 251 (1979), 187-218. | DOI | MR

[9] J. Marschall: Pseudo-differential operators with nonregular symbols. Thesis, FU Berlin (West), 1985.

[10] Y. Meyer: Remarques sur un théorème de J. M. Bony. Suppl. Rendiconti Circ. Mat. Palermo Serie II, 1 (1981), 1-20. | MR | Zbl

[11] S. Mizohata: Lectures on the Cauchy problem. Tata Institute, Bombay 1965. | MR

[12] J. Peetre: Interpolation of Lipschitz operators and metric spaces. Matematica (Cluj) 12 (35) (1970), 325-334. | MR | Zbl

[13] J. Peetre: On spaces of Triebel-Lizorkin type. Ark. Mat. 13 (1975), 123-130. | DOI | MR | Zbl

[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. | MR

[15] Th. Runst: Para-differential operators in spaces of Triebel-Lizorkin and Besov type. Z. Anal. Anwendungen 4 (1985), 557-573. | DOI | MR | Zbl

[16] Th. Runst: Mapping properties of non-linear operators in spaces of Triebel-Lizorkin and Besov type. Anal. Math. 12 (1986), 313-346. | DOI | MR

[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. | MR

[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. | MR

[19] G. Stampacchia: Equations elliptiques du second ordre à coefficients discontinues. Univ. Montreal Press, Quebec, 1966. | MR

[20] E. M. Stein: Singular integrals and differentiability properties of functions. Princeton Univ. Press, Princeton 1979. | MR

[21] H. Triebel: Theory of function spaces. Akad. Verlagsges. Geest and Portig K. G., Leipzig and Birkhäuser Verlag, Basel, Boston, Stuttgart 1983. | MR | Zbl

[22] H. Triebel: Mapping properties of non-linear operators generated by holomorphic $\Phi(u)$ in function spaces of Besov-Sobolev-Hardy type. Boundary value problems for elliptic differential equations of type $\Delta u = f(x) + \Phi(u)$. Math. Nachr. 117 (1984), 193-213. | DOI | MR

[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. | MR | Zbl

[24] M. Yamazaki: A quasi-homogeneous version of the microlocal analysis for nonlinear partial differential equations. Preprint. | MR | Zbl

Cité par Sources :