Fourier type and complex interpolation
HTML articles powered by AMS MathViewer
- by Mario Milman PDF
- Proc. Amer. Math. Soc. 89 (1983), 246-248 Request permission
Abstract:
Using Fourier type arguments we provide a very simple proof of recent results on complex interpolation of ${H^p}$ spaces and martingale ${H^p}$ spaces. The same method gives a new result on complex interpolation of Sobolev spaces.References
-
C. P. Calderón and M. Milman, Interpolation of Sobolev spaces. The real method, Indiana Univ. J. (to appear).
- R. DeVore and K. Scherer, Interpolation of linear operators on Sobolev spaces, Ann. of Math. (2) 109 (1979), no. 3, 583–599. MR 534764, DOI 10.2307/1971227
- C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193. MR 447953, DOI 10.1007/BF02392215
- Svante Janson and Peter W. Jones, Interpolation between $H^{p}$ spaces: the complex method, J. Functional Analysis 48 (1982), no. 1, 58–80. MR 671315, DOI 10.1016/0022-1236(82)90061-1
- Mario Milman, On the interpolation of martingale $L^{p}$ spaces, Indiana Univ. Math. J. 30 (1981), no. 2, 313–318. MR 604288, DOI 10.1512/iumj.1981.30.30025 —, Interpolation of martingale spaces and applications, 11 Sem. Bras. Anal. (Sao Carlos, 1980), pp. 92-108. —, Interpolation of some concrete scales of spaces, Technical Report, Univ. of Lund, 1982.
- Jaak Peetre, Sur la transformation de Fourier des fonctions à valeurs vectorielles, Rend. Sem. Mat. Univ. Padova 42 (1969), 15–26 (French). MR 256153
- N. M. Rivière and Y. Sagher, Interpolation between $L^{\infty }$ and $H^{1}$, the real method, J. Functional Analysis 14 (1973), 401–409. MR 0361759, DOI 10.1016/0022-1236(73)90053-0
- Thomas H. Wolff, A note on interpolation spaces, Harmonic analysis (Minneapolis, Minn., 1981) Lecture Notes in Math., vol. 908, Springer, Berlin-New York, 1982, pp. 199–204. MR 654187
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 89 (1983), 246-248
- MSC: Primary 46E35; Secondary 42B30, 46M35
- DOI: https://doi.org/10.1090/S0002-9939-1983-0712631-X
- MathSciNet review: 712631