Mapping properties of non-linear operators in spaces of Triebel-Lizorkin and Besov type

Analysis Mathematica - Tập 12 Số 4 - Trang 313-346 - 1986
Thomas Runst1
1Sektion Mathematik, Universität Jena, Jena, DDR

Tóm tắt

Từ khóa


Tài liệu tham khảo

D. R. Adams, On the existence of capacitary strong type estimates inR n ,Ark. Mat.,14 (1976), 125–140.

G.Bourdaud,Sur les opérateurs pseudo-différentiels à coefficients peu reguliers, Diss. Université de Paris-Sud (1983).

B. E. J.Dahlberg, A note on Sobolev spaces,Proc. Symp. in Pure Math. 35, part. 1, 183–185.

C. Fefferman andE. M. Stein, Some maximal inequalities,Amer. J. Math. 93 (1971), 107–115.

J. Franke, On the spacesF p,q s of Triebel — Lizorkin type: Pointwise multipliers and spaces on domains,Math. Nachr. 125 (1986), 29–68.

S. Fucik, J. Necas andV. Soucek,Einführung in die Variationsrechnung, Teubner (Leipzig, 1977).

B. Jawerth, Some observations on Besov and Lizorkin — Triebel spaces,Math. Scand.,40 (1977), 94–104.

G. A. Kaljabin, Criteria of the multiplication property and the embedding inC of spaces of Besov — Lizorkin — Triebel type (Russian),Mat. Zametki,30 (1981), 517–526.

M. A. Krasnoselski,Topological methods in the theory of nonlinear integral equations, Macmillan (New York, 1964).

Y.Meyer, Régularité des solutions des équations aux dérivées partielles non linéaires [d'après J.-M. Bony],Sem. Bourbaki, 32e année (1979–80), n∘. 560.

Y. Meyer, Remarques sur un théorème de J. M. Bony,Suppl. Rendiconti Circ. Mat. Palermo, Serie II, n∘.1 (1981), 1–20.

J. Peetre, Interpolation of Lipschitz operators and metric spaces,Matematica (Cluj)12 (35), (1970), 1–20.

T. Runst, Pseudo differential operators of the “exotic” classL 1,1 0 in spaces of Besov and Triebel — Lizorkin type,Annals of Global Analysis and Geometry 3 (1) (1985), 13–28. Mapping properties of non-linear operators in spaces of Triebel-Lizorkin and Besov type

T. Runst, Para-differential operators in spaces of Triebel — Lizorkin and Besov type,Z. Anal. Anwendungen 4 (1985), 557–573.

G. Stampacchia,Equations elliptiques du second ordre à coefficients discontinus, Univ. Montreal Press (Quebec, 1966).

H. Triebel,Fourier analysis and function spaces, Teubner (Leipzig, 1977).

H. Triebel,Spaces of Besov-Hardy-Sobolev type, Teubner (Leipzig, 1978).

H. Triebel,Theory of function spaces, Birkhäuser (Boston, 1983).

H.Triebel, Mapping properties of non-linear operators generated byΦ(u)=|u|ϱ and by holomorphicΦ(u) in function spaces of Besov-Hardy-Sobolev type. Boundary value problems for elliptic differential equations of type Δu=f(x)+Φ(u),Math. Nachr. 117 (1984).

H. Triebel,Interpolation theory, function spaces, differential operators, North-Holland (Amsterdam-New York-Oxford, 1978).

M. M. Vajnberg,Variational methods for the study of nonlinear operators, Holden-Day (San Francisco, 1964).