| Title:
|
On boundedness of superposition operators in spaces of Triebel-Lizorkin type (English) |
| Author:
|
Sickel, Winfried |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
1989 |
| Pages:
|
323-347 |
| . |
| Category:
|
math |
| . |
| MSC:
|
46E35 |
| MSC:
|
47H99 |
| idZBL:
|
Zbl 0693.46039 |
| idMR:
|
MR992137 |
| DOI:
|
10.21136/CMJ.1989.102305 |
| . |
| Date available:
|
2008-06-09T15:27:13Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/102305 |
| . |
| Reference:
|
[1] D. R. Adams: Qn the existence of capacitary strong type estimates in $R_n$.Ark. Mat. 14 (1976), 125-140. MR 0417774, 10.1007/BF02385830 |
| Reference:
|
[2] G. Bourdaud: Sur les opérateurs peudo-différentiels à coefficients peu réguliers.Diss. Univ. de Paris-Sud, 1983. |
| Reference:
|
[3] B. E. J. Dahlberg: A note on Sobolev spaces.Proc. Symp. Pure Math. 35, 1979, part I, 183-185. Zbl 0421.46027, MR 0545257 |
| Reference:
|
[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 0809954 |
| Reference:
|
[5] C. Fefferman, E. M. Stein: Some maximal inequalities.Amer. J. Math. 93 (1971), 107-115. Zbl 0222.26019, MR 0284802, 10.2307/2373450 |
| Reference:
|
[6] C. Fefferman, E. M. Stein: $H^p$ spaces of several variables.Acta Math. 129 (1972), 137-193. MR 0447953, 10.1007/BF02392215 |
| Reference:
|
[7] M. Marcus, V. J. Mizel: Absolute continuity on tracks and mappings of Sobolev spaces.Rational Mech. Anal. 42 (1972), 294-320. Zbl 0236.46033, MR 0338765, 10.1007/BF00251378 |
| Reference:
|
[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. MR 0531975, 10.1090/S0002-9947-1979-0531975-1 |
| Reference:
|
[9] J. Marschall: Pseudo-differential operators with nonregular symbols.Thesis, FU Berlin (West), 1985. |
| Reference:
|
[10] Y. Meyer: Remarques sur un théorème de J. M. Bony.Suppl. Rendiconti Circ. Mat. Palermo Serie II, 1 (1981), 1-20. Zbl 0473.35021, MR 0639462 |
| Reference:
|
[11] S. Mizohata: Lectures on the Cauchy problem.Tata Institute, Bombay 1965. MR 0219881 |
| Reference:
|
[12] J. Peetre: Interpolation of Lipschitz operators and metric spaces.Matematica (Cluj) 12 (35) (1970), 325-334. Zbl 0217.44504, MR 0482280 |
| Reference:
|
[13] J. Peetre: On spaces of Triebel-Lizorkin type.Ark. Mat. 13 (1975), 123-130. Zbl 0302.46021, MR 0380394, 10.1007/BF02386201 |
| Reference:
|
[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 0730621 |
| Reference:
|
[15] Th. Runst: Para-differential operators in spaces of Triebel-Lizorkin and Besov type.Z. Anal. Anwendungen 4 (1985), 557-573. Zbl 0592.35011, MR 0818984, 10.4171/ZAA/175 |
| Reference:
|
[16] Th. Runst: Mapping properties of non-linear operators in spaces of Triebel-Lizorkin and Besov type.Anal. Math. 12 (1986), 313-346. MR 0877164, 10.1007/BF01909369 |
| Reference:
|
[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 0932288 |
| Reference:
|
[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 1066752 |
| Reference:
|
[19] G. Stampacchia: Equations elliptiques du second ordre à coefficients discontinues.Univ. Montreal Press, Quebec, 1966. MR 0251373 |
| Reference:
|
[20] E. M. Stein: Singular integrals and differentiability properties of functions.Princeton Univ. Press, Princeton 1979. MR 0290095 |
| Reference:
|
[21] H. Triebel: Theory of function spaces.Akad. Verlagsges. Geest and Portig K. G., Leipzig and Birkhäuser Verlag, Basel, Boston, Stuttgart 1983. Zbl 0546.46028, MR 0781540 |
| Reference:
|
[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. MR 0755303, 10.1002/mana.3211170115 |
| Reference:
|
[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. Zbl 0608.47058, MR 0837335 |
| Reference:
|
[24] M. Yamazaki: A quasi-homogeneous version of the microlocal analysis for nonlinear partial differential equations.Preprint. Zbl 0701.35162, MR 0977891 |
| . |
