Anisotropic function spaces and related semi-linear hypoelliptic equations

Mathematische Nachrichten

Volumn 248-249, Issue , 2003, Pages 40-61

  Dachkovski, Serguei ^a  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

Anisotropic function space; Fatou property; Fubini property

Indexed keywords

EID: 0037283683     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.200310002     Document Type: Article

References (21)

1. O. V. Besov, V. P. Ilyin, and S. M. Nikolski, Integral Representations of Functions and Embedding Theorems (Russian), (Nauka, Moscow, 1975).
2. P. Dintelmann, Classes of Fourier multipliers and Besov-Nikolskij spaces, Math. Nachr. 173, 115-130 (1995).
3. D. E. Edmunds and H. Triebel, Function Spaces, Entropy Numbers, Differential Operators, (Cambridge University Press, 1996).
4. W. Farkas, Atomic and subatomic decompositions in anisotropic function spaces, Math. Nachr. 209, 83-113 (2000).
5. R. Hochmuth, Wavelet characterization for anisotropic Besov spaces, to appear (2001).
6. T. D. Long and H. Triebel, Equivalent norms and Schauder bases in anisotropic Besov spaces, in: Proceedings of the Royal Society of Edinburgh 84A (1979), p. 177-183.
7. S. M. Nikolski, Approximation of Functions of Several Variables and Embedding Theorems (Russian), second edition (Nauka, Moscow, 1977).
8. T. Runst and W. Sickel, Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Operators (Walter de Gruyter, Berlin, 1996).
9. H.-J. Schmeisser, Anisotropic spaces II. Equivalent norms for abstract spaces, function spaces with weights of Sobolev-Besov type, Math. Nachr. 79, 55-73 (1977).
10. s type, Math. Nachr. 80, 247-267 (1979).
11. H. J. Schmeisser and H. Triebel, Topics in Fourier Analysis and Function Spaces (Geest & Portig, Leipzig, 1987).
12. s type, Journal for Analysis and its Applications 14(1), 105-140 (1995).
13. H. Triebel, Fourier Analysis and Function Spaces (Teubner, Leipzig, 1977).
14. H. Triebel, Theory of Function Spaces (Birkhäuser, Basel, 1983).
15. H. Triebel, Theory of Function Spaces II (Birkhäuser, Basel, 1992).
16. H. Triebel, Fractals and Spectra (Birkhäuser, Basel, 1997).
17. H. Triebel, Truncations of functions, Forum Math 12, 731-756 (2000).
18. H. Triebel, Regularity theory for some semi-linear equations: the Q-method, Forum Math. 13, 1-19 (2001).
19. H. Triebel, The Structure of Functions (Birkhäuser, Basel, 2001).
20. H. Triebel, Refined solutions of some integral equations, Functiones et Approximation, to appear (2002).
21. M. Yamazaki, A quasi-homogeneous version of paradifferential operators, 1. Boundedness on spaces of Besov type, J. Fac. Sci. Univ. Tokyo, Sect. I. A, Math. 33, 131-174 (1986).