Geodesic
A Failure of Stability Under Complex Interpolation
Canadian journal of mathematics, Tome 29 (1977) no. 6, pp. 1167-1170

Voir la notice de l'article provenant de la source Cambridge University Press

Let denote the spaces of Bessel potentials as denned and discussed in [6]. When 1 < q < ∞ and α is an integer , the Sobolev space which consists of functions Fin Lq with α derivatives in Lq and with norm If now we make the change of variables x = ev, f(x) = F (In x) it is easily seen that the ratio 
Connett, William C.; Schwartz, Alan L. A Failure of Stability Under Complex Interpolation. Canadian journal of mathematics, Tome 29 (1977) no. 6, pp. 1167-1170. doi: 10.4153/CJM-1977-117-9
@article{10_4153_CJM_1977_117_9,
     author = {Connett, William C. and Schwartz, Alan L.},
     title = {A {Failure} of {Stability} {Under} {Complex} {Interpolation}},
     journal = {Canadian journal of mathematics},
     pages = {1167--1170},
     year = {1977},
     volume = {29},
     number = {6},
     doi = {10.4153/CJM-1977-117-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-117-9/}
}
TY  - JOUR
AU  - Connett, William C.
AU  - Schwartz, Alan L.
TI  - A Failure of Stability Under Complex Interpolation
JO  - Canadian journal of mathematics
PY  - 1977
SP  - 1167
EP  - 1170
VL  - 29
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-117-9/
DO  - 10.4153/CJM-1977-117-9
ID  - 10_4153_CJM_1977_117_9
ER  - 
%0 Journal Article
%A Connett, William C.
%A Schwartz, Alan L.
%T A Failure of Stability Under Complex Interpolation
%J Canadian journal of mathematics
%D 1977
%P 1167-1170
%V 29
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-117-9/
%R 10.4153/CJM-1977-117-9
%F 10_4153_CJM_1977_117_9

[1] 1. Calderôn, A., Intermediate spaces and interpolation, the complex method, Studia Math., 24 (1964), 113–190. Google Scholar

[2] 2. Connett, W. C. and Schwartz, A. L., A multiplier theorem for ultraspherical series, Studia Math. 51 (1974), 51–70. Google Scholar

[3] 3. Connett, W. C. and Schwartz, A. L. The theory of ultras pherical multipliers, Memoirs of the Amer. Math. Soc. 183 (1977). Google Scholar

[4] 4. Littman, W., Multipliers in and interpolation, Bull. Amer. Math. Soc. 71 (1965), 764–766. Google Scholar

[5] 5. Peetre, J., Applications de la théorie des espaces d'interpolation, Ricerche de Mathematica, 15 (1966), 3–36. Google Scholar

[6] 6. Stein, E. M., Singular integrals and differentiability properties of functions (Princeton University Press, 1970). Google Scholar

[7] 7. Strichartz, R., Multipliers for spherical harmonic expansions, Trans. Am. Math. Soc. 167 (1972), 115–124. Google Scholar

[8] 8. Zygmund, A., Trigonometric series, vol. I (Cambridge University Press, 1959). Google Scholar

Cité par Sources :