Hankel multiplier transformations and weighted $p$-norms
HTML articles powered by AMS MathViewer
- by Douglas L. Guy
- Trans. Amer. Math. Soc. 95 (1960), 137-189
- DOI: https://doi.org/10.1090/S0002-9947-1960-0120506-1
- PDF | Request permission
References
- S. Bochner, Positive zonal functions on spheres, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 1141–1147. MR 68127, DOI 10.1073/pnas.40.12.1141
- S. Bochner and K. Chandrasekharan, Fourier Transforms, Annals of Mathematics Studies, No. 19, Princeton University Press, Princeton, N. J.; Oxford University Press, London, 1949. MR 0031582 Delsarte 1938. Sur une extension de la formula de Taylor, J. Math. Pures Appl. vol. 171, pp. 213-231. Erdélyi, W. Magnus, F. Oberhettinger and F. Tricomi 1953. Higher transcendental functions, vol. 1, New York.
- G. H. Hardy and J. E. Littlewood, Some more theorems concerning Fourier series and Fourier power series, Duke Math. J. 2 (1936), no. 2, 354–382. MR 1545928, DOI 10.1215/S0012-7094-36-00228-4
- G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge, at the University Press, 1952. 2d ed. MR 0046395
- I. I. Hirschman, The decomposition of Walsh and Fourier series, Mem. Amer. Math. Soc. 15 (1955), 65. MR 72269
- I. I. Hirschman Jr., Weighted quadratic norms and Legendre polynomials, Canadian J. Math. 7 (1955), 462–482. MR 73731, DOI 10.4153/CJM-1955-050-x
- I. I. Hirschman Jr., A note on orthogonal systems, Pacific J. Math. 6 (1956), 47–56. MR 79129, DOI 10.2140/pjm.1956.6.47 Harmonic analysis and ultraspherical polynomials, Symposium on Harmonic Analysis and Related Integral Transforms held at Cornell University, vol. 1.
- I. I. Hirschman Jr., Projections associated with Jacobi polynomials, Proc. Amer. Math. Soc. 8 (1957), 286–290. MR 85359, DOI 10.1090/S0002-9939-1957-0085359-4
- Richard Askey and Isidore Hirschman Jr., Weighted quadratic norms and ultraspherical polynomials. I, Trans. Amer. Math. Soc. 91 (1959), 294–313. MR 107772, DOI 10.1090/S0002-9947-1959-0107772-5
- B. M. Levitan, The application of generalized displacement operators to linear differential equations of the second order, Amer. Math. Soc. Translation 1951 (1951), no. 59, 135. MR 0044707 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. H. Loomis 1953. Abstract harmonic analysis, New York. Marcinkiewicz 1939. Sur les multiplicateurs des séries de Fourier, Studia Math. vol. 8, pp. 78-91. E. A. C. Paley 1931. Some theorems on orthogonal functions, Studia Math. vol. 3, pp. 226-239.
- Harry Pollard, The mean convergence of orthogonal series. I, Trans. Amer. Math. Soc. 62 (1947), 387–403. MR 22932, DOI 10.1090/S0002-9947-1947-0022932-1
- Harry Pollard, The mean convergence of orthogonal series. II, Trans. Amer. Math. Soc. 63 (1948), 355–367. MR 23941, DOI 10.1090/S0002-9947-1948-0023941-X
- Harry Pollard, The mean convergence of orthogonal series. III, Duke Math. J. 16 (1949), 189–191. MR 28459
- Friedrich Riesz, Über eine Verallgemeinerung der Parsevalschen Formel, Math. Z. 18 (1923), no. 1, 117–124 (German). MR 1544624, DOI 10.1007/BF01192400 Sur la formule d’inversion de Fourier, Acta Sci. Math. Szeged vol. 3, pp. 235-241.
- Ian N. Sneddon, Fourier Transforms, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1951. MR 0041963
- S. B. Stečkin, On bilinear forms, Doklady Akad. Nauk SSSR (N.S.) 71 (1950), 237–240 (Russian). MR 0033868 C. Titchmarsh 1922. Hankel transforms, Proc. London Math. Soc. vol. 45, pp. 458-474. The theory of Fourier integrals, Oxford.
- Daniel Waterman, On functions analytic in a half-plane, Trans. Amer. Math. Soc. 81 (1956), 167–194. MR 76030, DOI 10.1090/S0002-9947-1956-0076030-7 N. Watson 1944. The theory of Bessel functions, Cambridge.
- G. Milton Wing, The mean convergence of orthogonal series, Amer. J. Math. 72 (1950), 792–808. MR 37923, DOI 10.2307/2372296
- G. M. Wing, On the $L^p$ theory of Hankel transforms, Pacific J. Math. 1 (1951), 313–319. MR 43934, DOI 10.2140/pjm.1951.1.313 Zygmund 1935. Trigonometrical series, Warsaw-Lwow. On the convergence and summability of power series on the circle of convergence I, Fund. Math. vol. 30, pp. 170-196.
- A. Zygmund, Proof of a theorem of Littlewood and Paley, Bull. Amer. Math. Soc. 51 (1945), 439–446. MR 12306, DOI 10.1090/S0002-9904-1945-08374-8
Bibliographic Information
- © Copyright 1960 American Mathematical Society
- 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