Analytic families of operators on some quasi-Banach spaces

Cwikel, Michael; Sagher, Yoram

doi:10.1090/S0002-9939-1988-0934878-4

Analytic families of operators on some quasi-Banach spaces
HTML articles powered by AMS MathViewer

by Michael Cwikel and Yoram Sagher

Proc. Amer. Math. Soc. 102 (1988), 979-984

DOI: https://doi.org/10.1090/S0002-9939-1988-0934878-4

PDF | Request permission

Abstract:

An interpolation theorem for analytic families of operators on some quasi-Banach spaces is proved. The result is applicable to spaces whose quasi-norm is defined by means of a maximal function, for example the various ${H_p}$ spaces on locally compact groups.

References

A.-P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113–190. MR 167830, DOI 10.4064/sm-24-2-113-190
R. R. Coifman, M. Cwikel, R. Rochberg, Y. Sagher, and G. Weiss, A theory of complex interpolation for families of Banach spaces, Adv. in Math. 43 (1982), no. 3, 203–229. MR 648799, DOI 10.1016/0001-8708(82)90034-2
Michael Cwikel and Svante Janson, Interpolation of analytic families of operators, Studia Math. 79 (1984), no. 1, 61–71. MR 772005, DOI 10.4064/sm-79-1-61-71
M. Cwikel, M. Milman, and Y. Sagher, Complex interpolation of some quasi-Banach spaces, J. Funct. Anal. 65 (1986), no. 3, 339–347. MR 826431, DOI 10.1016/0022-1236(86)90023-6
I. I. Hirschman Jr., A convexity theorem for certain groups of transformations, J. Analyse Math. 2 (1953), 209–218. MR 57936, DOI 10.1007/BF02825637
N. J. Kalton, Convexity conditions for nonlocally convex lattices, Glasgow Math. J. 25 (1984), no. 2, 141–152. MR 752808, DOI 10.1017/S0017089500005553
N. J. Kalton, Plurisubharmonic functions on quasi-Banach spaces, Studia Math. 84 (1986), no. 3, 297–324. MR 877084, DOI 10.4064/sm-84-3-297-324
Yoram Sagher, On analytic families of operators, Israel J. Math. 7 (1969), 350–356. MR 257822, DOI 10.1007/BF02788866

Interpolation of some analytic families of operators

Elias M. Stein, Interpolation of linear operators, Trans. Amer. Math. Soc. 83 (1956), 482–492. MR 82586, DOI 10.1090/S0002-9947-1956-0082586-0