Publication:
Abstract and Concrete Logarithmic Interpolation Spaces

Loading...
Thumbnail Image
Full text at PDC
Publication Date
2004
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Oxford University Press
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
A procedure is given to reduce the interpolation spaces on an ordered pair generated by the function parameter tθ (1 + |log t|)−b to the classical real interpolation spaces. Applications are given for Lorentz–Zygmund function spaces, Besov spaces of generalized smoothness and Lorentz– Zygmund operator spaces.
Description
Keywords
Citation
C. Bennett and K. Rudnick, ‘On Lorentz–Zygmund spaces’, Dissertationes Math. 175 (1980) 1–67. C. Bennett and R. Sharpley, Interpolation of operators (Academic Press, Boston, 1988). J. Bergh and J. L¨ofstr¨om, Interpolation spaces. An introduction (Springer, Berlin, 1976). M. Bricchi, ‘Tailored Besov spaces and h-sets’, Math. Nachr. 263–4 (2004) 36–52. M. Bricchi and S. D. Moura, ‘Complements on growth envelopes of spaces with generalised smoothness in the sub-critical case’, Z. Anal. Anwendungen 22 (2003) 383–398. A. M. Caetano and S. D. Moura, ‘Local growth envelopes of spaces of generalised smoothness: the sub-critical case’, Math. Nachr., to appear. F. Cobos, ‘On the Lorentz–Marcinkiewicz operator ideal’, Math. Nachr. 126 (1986) 281–300. logarithmic interpolation spaces 243 F. Cobos, ‘Entropy and Lorentz–Marcinkiewicz operator ideals’, Ark. Mat. 25 (1987) 211– 219. F. Cobos, ‘Duality and Lorentz–Marcinkiewicz operator spaces’, Math. Scand. 63 (1988) 261–267. F. Cobos and D. L. Fernandez, ‘Hardy–Sobolev spaces and Besov spaces with a function parameter’, Lecture Notes in Mathematics 1302 (Springer, Berlin, 1988) 158–170. F. Cobos, L. M. Fern´andez-Cabrera, F. L. Hern´andez and V. M. S´anchez, ‘Indices defined by interpolation scales and applications’, Proc. Roy. Soc. Edinburgh, to appear. D. E. Edmunds and H. Triebel, Function spaces, entropy numbers, differential operators (Cambridge University Press, Cambridge, 1996). D. E. Edmunds and H. Triebel, ‘Logarithmic spaces and related trace problems’, Funct. Approx. Comment. Math. 26 (1998) 189–204. L. M. Fern´andez-Cabrera, ‘Inclusion indices of function spaces and applications’, Math. Proc. Cambridge Philos. Soc. 136 (2004) 665–674. I. C. Gohberg and M. G. Krein, Introduction to the theory of linear nonselfadjoint operators (American Mathematical Society, Providence, RI, 1969). J. Gustavsson, ‘A function parameter in connection with interpolation of Banach spaces’, Math. Scand. 42 (1978) 289–305. D. D. Haroske and S. D. Moura, ‘Continuity envelopes of spaces of generalised smoothness, entropy and approximation numbers’, Preprint, Friedrich-Schiller-Universit¨at Jena, 2003. S. Janson, ‘Minimal and maximal methods of interpolation’, J. Funct. Anal. 44 (1981) 50–73. B. Jawerth and M. Milman, ‘Extrapolation theory with applications’, Mem. Amer. Math. Soc. 440 (1991). H. K¨onig, Eigenvalue distribution of compact operators (Birkh¨auser, Basel, 1986). C. Merucci, ‘Applications of interpolation with a function parameter to Lorentz, Sobolev and Besov spaces’, Lecture Notes in Mathematics 1070 (Springer, Berlin, 1984) 183–201. M. Milman, Extrapolation and optimal decompositions, Lecture Notes in Mathematics 1580 (Springer, Berlin, 1994). S. Moura, ‘Function spaces of generalised smoothness’, Dissertationes Math. 398 (2001) 1–88. L.-E. Persson, ‘Interpolation with a parameter function’, Math. Scand. 59 (1986) 199–222. A. Pietsch, Eigenvalues and s-numbers (Cambridge University Press, Cambridge, 1987). H. Triebel, ‘¨Uber die Verteilung der Approximationszahlen kompakter Operatoren in Sobolev–Besov–R¨aumen’, Invent. Math. 4 (1967) 275–279. H. Triebel, Interpolation theory, function spaces, differential operators (North-Holland, Amsterdam, 1978), 2nd edn. (Barth, Leipzig, 1995). H. Triebel, Theory of function spaces (Birkh¨auser, Basel, 1983). H. Triebel, Theory of function spaces II (Birkh¨auser, Basel, 1992). H. Triebel, The structure of functions (Birkh¨auser, Basel, 2001)
Collections