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Hankel multiplier transformations and weighted $ p$-norms


Author: Douglas L. Guy
Journal: Trans. Amer. Math. Soc. 95 (1960), 137-189
MSC: Primary 44.00
DOI: https://doi.org/10.1090/S0002-9947-1960-0120506-1
MathSciNet review: 0120506
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  • [S] Bochner 1954. Positive zonal function on spheres, Proc. Nat. Acad. Sci. U.S.A. vol. 40, pp. 1141-1147. MR 0068127 (16:834e)
  • [S] Bochner and K. Chandrasekharan 1949. Fourier transforms, Princeton. MR 0031582 (11:173d)
  • [J] Delsarte 1938. Sur une extension de la formula de Taylor, J. Math. Pures Appl. vol. 171, pp. 213-231.
  • [A] Erdélyi, W. Magnus, F. Oberhettinger and F. Tricomi 1953. Higher transcendental functions, vol. 1, New York.
  • [G] Hardy and J. Littlewood 1936. Some more theorems concerning Fourier series, Duke Math. J. vol. 2, pp. 354-382. MR 1545928
  • [G] Hardy, J. Littlewood and G. Polya 1952. Inequalities, Cambridge. MR 0046395 (13:727e)
  • [I] I. Hirschman, Jr. 1955a. The Decomposition of Walsh and Fourier series, Memoirs Amer. Math. Soc., no. 15, 65 pp. MR 0072269 (17:257e)
  • [1955b] Weighted quadratic norms and Legendre polynomials, Canad. J. Math. vol. 7, pp. 462-482. MR 0073731 (17:477b)
  • [1956a] A note on orthogonal systems, Pacific J. Math. vol. 6, pp. 47-56. MR 0079129 (18:33c)
  • [1956b] Harmonic analysis and ultraspherical polynomials, Symposium on Harmonic Analysis and Related Integral Transforms held at Cornell University, vol. 1.
  • [1957] Projections associated with Jacobi polynomials, Proc. Amer. Math. Soc. vol. 8, pp. 286-290. MR 0085359 (19:27c)
  • [I] I. Hirschman Jr. and R. Askey 1959. Weighted quadratic norms and ultraspherical polynomials, Trans. Amer. Math. Soc. vol. 91, pp. 294-313. MR 0107772 (21:6494)
  • [B] M. Levitan 1949. The application of generalized displacement operators to linear differential equations of second order, Amer. Math. Soc. Translations, no. 59. MR 0044707 (13:463g)
  • [J] Littlewood and R. E. A. C. Paley 1937. Theorems on Fourier series and power series II, Proc. London Math. Soc. vol. 42, pp. 52-89.
  • [L] H. Loomis 1953. Abstract harmonic analysis, New York.
  • [J] Marcinkiewicz 1939. Sur les multiplicateurs des séries de Fourier, Studia Math. vol. 8, pp. 78-91.
  • [R] E. A. C. Paley 1931. Some theorems on orthogonal functions, Studia Math. vol. 3, pp. 226-239.
  • [H] Pollard 1947. The mean convergence of orthogonal series, Trans. Amer. Math. Soc. vol. 62, pp. 387-403. MR 0022932 (9:280d)
  • [1948] The mean convergence of orthogonal series. II, Trans. Amer. Math. Soc. vol. 63, pp. 355-367. MR 0023941 (9:426e)
  • [1949] The mean convergence of orthogonal series. III, Duke Math. J. vol. 16, pp. 189-191. MR 0028459 (10:450d)
  • [M] Riesz 1923. Über eine Verallgemeinerung der Parsevalschen Formel, Math. Z. vol. 18, pp. 117-124. MR 1544624
  • [1927] Sur la formule d'inversion de Fourier, Acta Sci. Math. Szeged vol. 3, pp. 235-241.
  • [I] N. Sneddon 1951. Fourier transforms, New York. MR 0041963 (13:29h)
  • [S] B. Stečkin 1950. On bilinear forms, Dokl. Akad. Nauk SSSR, N.S. vol. 71, pp. 237-240. MR 0033868 (11:504c)
  • [E] C. Titchmarsh 1922. Hankel transforms, Proc. London Math. Soc. vol. 45, pp. 458-474.
  • [1937] The theory of Fourier integrals, Oxford.
  • [D] Waterman 1956. On functions analytic in a half plane, Trans. Amer. Math. Soc. vol. 81, pp. 167-194. MR 0076030 (17:834f)
  • [G] N. Watson 1944. The theory of Bessel functions, Cambridge.
  • [G] M. Wing 1950. The mean convergence of orthogonal series, Amer. J. Math. vol. 72, pp. 792-807. MR 0037923 (12:329e)
  • [1951] On the $ {L_p}$ theory of Hankel transforms, Pacific J. Math. vol. 1, pp. 313-319. MR 0043934 (13:342b)
  • [A] Zygmund 1935. Trigonometrical series, Warsaw-Lwow.
  • [1938] On the convergence and summability of power series on the circle of convergence I, Fund. Math. vol. 30, pp. 170-196.
  • [1945] Proof of a theorem of Littlewood and Paley, Bull. Amer. Math. Soc. vol. 51, pp. 439-446. MR 0012306 (7:8b)

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DOI: https://doi.org/10.1090/S0002-9947-1960-0120506-1
Article copyright: © Copyright 1960 American Mathematical Society

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