## Interpolation of linear operators.(English)Zbl 0072.32402

### Keywords:

Functional Analysis; Abstract Spaces
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### References:

 [1] S. Banach, Théorie des opérations linéaires, Warsaw, 1932. · JFM 58.0420.01 [2] Salomon Bochner, Summation of multiple Fourier series by spherical means, Trans. Amer. Math. Soc. 40 (1936), no. 2, 175 – 207. · Zbl 0015.15702 [3] A. P. Calderón and A. Zygmund, On the theorem of Hausdorff-Young and its extensions, Contributions to Fourier Analysis, Annals of Mathematics Studies, no. 25, Princeton University Press, Princeton, N. J., 1950, pp. 166 – 188. [4] I. I. Hirschman Jr., Weighted quadratic norms and Legendre polynomials, Canad. J. Math. 7 (1955), 462 – 482. · Zbl 0067.04101 [5] I. I. Hirschman Jr., A convexity theorem for certain groups of transformations, J. Analyse Math. 2 (1953), 209 – 218. · Zbl 0052.06302 [6] -, Decomposition of Walsh and Fourier series, Memoirs of the American Mathematical Society, no. 15. · Zbl 0067.04102 [7] H. R. Pitt, Theorems on Fourier series and power series, Duke Math. J. 3 (1937), no. 4, 747 – 755. · Zbl 0018.01703 [8] M. Riesz, Sur les maximas des formes bilinéaires et sur les fonctionelles linéaires, Acta Math. vol. 49 (1926) pp. 464-497. · JFM 53.0259.03 [9] J. D. Tamarkin and A. Zygmund, Proof of a theorem of Thorin, Bull. Amer. Math. Soc. 50 (1944), 279 – 282. · Zbl 0060.24104 [10] G. O. Thorin, An extension of a convexity theorem due to M. Riesz, Kungl. Fysiografiska Saellskapets i Lund Förhandlingar, no. 14, vol. 8 (1939). · JFM 65.0215.02 [11] -, Convexity theorems, Uppsala, 1948, pp. 1-57. [12] G. N. Watson, A treatise on the theory of Bessel functions, Cambridge, 1922. · JFM 48.0412.02 [13] A. Zygmund, Trigonometrical series, Warsaw, 1935. · Zbl 0011.01703
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