This is a preview of subscription content, log in via an institution to check access.
Literature Cited
G. Fefferman and H. Shapiro, “A planar face on the sphere of the multiplier space Mp, 1<p<∞,” Proc. Am. Math. Soc.,36, No. 2, 435–439 (1972).
I. Segal, “Construction of nonlinear local quantum processes. I,” Ann. Math.,92, 462–481 (1970).
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. II, Academic Press, New York (1975).
E. M. Semenov and I. Ya. Shneiberg, “Hypercontractive operators and the Khinchin inequality,” Funkts. Anal. Prilozh.,22, No. 3, 87–88 (1988).
S. G. Krein, Yu. I. Petunin, and E. M. Semenov, Interpolation of Linear Operators [in Russian], Nauka, Moscow (1976).
J. Diestel, Geometry of Banach Spaces, Springer, Berlin (1975).
J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, II: Function Spaces, Springer, Berlin (1979).
R. E. Edwards, Fourier Series. A Modern Introduction, Vol. II, Holt, Rinehart, and Winston, New York (1967).
D. Lamberton, “Spectres d'operatéurs de convolution definis LP a valeurs vectorielles,” C. R. Acad. Sci. Paris,296, 125–128 (1983).
D. Lamberton, “Spectres d'opérateurs et geometric des espaces de Banach,” Dissertationes Math.,242, 1–58 (1985).
A. V. Bukhvalov, “Continuity of operators in spaces of measurable vector-valued functions with applications to the investigation of Sobolev spaces and analytic functions in the vector-valued case,” Dokl. Akad. Nauk SSSR,246, No. 3, 524–528 (1979).
P. P. Zabreiko, “On the spectrum of linear operators acting in different Banach spaces,” In: Qualitative and Approximate Methods for the Investigation of Operator Equations [in Russian], Yaroslavl' State Univ., Yaroslavl' (1976), pp. 39–47.
P. Sarnak, “Spectra of singular measures as multipliers on LP,” J. Funct. Anal.,37, 302–317 (1980).
W. Beckner, “Inequalities in Fourier analysis,” Ann. Math.,107, 159–182 (1975).
A. Zygmund, Trigonometric Series, Vol. I, Cambridge Univ. Press, Cambridge (1959).
J.-P. Kahane, Some Random Series of Functions, Heath and Co., Lexington, Mass. (1965).
I. K. Matsak and A. N. Plichko, “Lp-inequalities for sums of random variables,” Teor. Veroyatn, Primenen.,32, No. 1, 197 (1987).
Additional information
Voronezh. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 1, pp. 141–149, January–February, 1990.
Rights and permissions
About this article
Cite this article
Semenov, E.M., Shneiberg, I.Y. Contractive operators and Khinchin's inequality. Sib Math J 31, 119–127 (1990). https://doi.org/10.1007/BF00971157
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00971157