PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1999 | 136 | 1 | 17-35
Tytuł artykułu

Interpolation of real method spaces via some ideals of operators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Certain operator ideals are used to study interpolation of operators between spaces generated by the real method. Using orbital equivalence a new reiteration formula is proved for certain real interpolation spaces generated by ordered pairs of Banach lattices of the form $(X,L_∞(w))$. As an application we extend Ovchinnikov's interpolation theorem from the context of classical Lions-Peetre spaces to a larger class of real interpolation spaces. A description of certain abstract J-method spaces is also presented.
Słowa kluczowe
Czasopismo
Rocznik
Tom
136
Numer
1
Strony
17-35
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-06-20
Twórcy
  • Faculty of Mathematics and Computer Science, A. Mickiewicz University, Matejki 48/49 60-769 Poznań, Poland , mastylo@math.amu.edu.pl
autor
Bibliografia
  • [1] G. Bennett, Inclusion mappings between $l^p$ spaces, J. Funct. Anal. 13 (1973), 20-27.
  • [2] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin, 1976.
  • [3] Yu. A. Brudnyĭ and N. Ya. Krugljak, Interpolation Functors and Interpolation Spaces I, North-Holland, Amsterdam, 1991.
  • [4] A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113-190.
  • [5] M. Cwikel and J. Peetre, Abstract K and J spaces, J. Math. Pures Appl. 60 (1981), 1-50.
  • [6] M. Cwikel and Y. Sagher, Relation between real and complex interpolation spaces, Indiana Univ. Math. J. 36 (1987), 905-912.
  • [7] V. I. Dmitriev, Duality of the interpolation methods of constants and means, Dokl. Akad. Nauk SSSR 214 (1974), 22-24 (in Russian).
  • [8] S. Janson, Maximal and minimal methods of interpolation, J. Funct. Anal. 44 (1981), 50-73.
  • [9] S. G. Kreĭn, Yu. I. Petunin and E. M. Semenov, Interpolation of Linear Operators, Nauka, Moscow, 1978 (in Russian); English transl.: Amer. Math. Soc., Providence, 1982.
  • [10] G. Ya. Lozanovskiĭ, On some Banach lattices IV, Sibirsk. Mat. Zh. 14 (1973), 140-155 (in Russian); English transl.: Siberian Math. J. 14 (1973), 97-108.
  • [11] L. Maligranda and M. Mastyło, Inclusion mappings between Orlicz sequence spaces, Report No. 090/1998, 12 pp., Faculty of Math. & Comp. Sci., Poznań.
  • [12] V. I. Ovchinnikov, The methods of orbits in interpolation theory, Math. Rep. 1 (1984), 349-516.
  • [13] V. I. Ovchinnikov, Interpolation theorems for $L_p,q$-spaces, Mat. Sb. 136 (1988), 227-240 (in Russian).
  • [14] A. Pietsch, Operator Ideals, North-Holland, Berlin, 1978.
  • [15] Y. Sagher, Interpolation of r-Banach spaces, Studia Math. 41 (1972), 45-70.
  • [16] G. Sparr, Interpolation of weighted $L_p$-spaces, ibid. 62 (1978), 229-271.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv136i1p17bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.