Analytic families of operators on some quasi-Banach spaces

Authors:
Michael Cwikel and Yoram Sagher

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

MSC:
Primary 46M35; Secondary 42B30, 46E10

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

MathSciNet review:
934878

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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 spaces on locally compact groups.

**[1]**A. P. Calderón,*Intermediate spaces and interpolation, the complex method*, Studia Math.**24**(1964), 113-190. MR**0167830 (29:5097)****[2]**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), 203-229. MR**648799 (83j:46084)****[3]**M. Cwikel and S. Janson,*Interpolation of analytic families of operators*, Studia Math.**79**(1984), 61-71. MR**772005 (86f:46082)****[4]**M. Cwikel, M. Milman and Y. Sagher,*Complex interpolation of some quasi-Banach spaces*, J. Funct. Anal.**65**(1986), 339-347. MR**826431 (87h:46152)****[5]**I. I. Hirschman,*A convexity theorem for certain groups of transformations*, J. Analyse Math.**2**(1953), 209-218. MR**0057936 (15:295b)****[6]**N. J. Kalton,*Convexity theorems for non-locally convex lattices*, Glasgow Math. J.**258**(1984), 141-152. MR**752808 (85h:46018)****[7]**-,*Plurisubharmonic functions on quasi-Banach spaces*, Studia Math. (to appear). MR**877084 (88g:46030)****[8]**Y. Sagher,*On analytic families of operators*, Israel J. Math.**7**(1969), 350-356. MR**0257822 (41:2471)****[9]**-,*Interpolation of some analytic families of operators*, Proc. U.S. Swedish Seminar on Function Spaces and Applications, Lecture Notes in Math., vol. 1302, Springer.**[10]**E. M. Stein,*Interpolation of linear operators*, Trans. Amer. Math. Soc.**83**(1956), 482-492. MR**0082586 (18:575d)**

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Additional Information

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

Article copyright:
© Copyright 1988
American Mathematical Society