Norm inequalities for some orthogonal series
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- by Richard Askey PDF
- Bull. Amer. Math. Soc. 72 (1966), 808-823
References
- Richard Askey and I. I. Hirschman Jr., Mean summability for ultraspherical polynomials, Math. Scand. 12 (1963), 167–177. MR 164198, DOI 10.7146/math.scand.a-10680
- Richard Askey and Stephen Wainger, Mean convergence of expansions in Laguerre and Hermite series, Amer. J. Math. 87 (1965), 695–708. MR 182834, DOI 10.2307/2373069
- Richard Askey and Stephen Wainger, On the behavior of special classes of ultraspherical expansions. I, II, J. Analyse Math. 15 (1965), 193–220. MR 193290, DOI 10.1007/BF02787693
- Richard Askey and Stephen Wainger, On the behavior of special classes of ultraspherical expansions. I, II, J. Analyse Math. 15 (1965), 193–220. MR 193290, DOI 10.1007/BF02787693
- Richard Askey and Stephen Wainger, A transplantation theorem between ultraspherical series, Illinois J. Math. 10 (1966), 322–344. MR 211187
- Richard Askey and Stephen Wainger, A transplantation theorem for ultraspherical coefficients, Pacific J. Math. 16 (1966), 393–405. MR 217508
- Richard Askey and Stephen Wainger, Integrability theorems for Fourier series, Duke Math. J. 33 (1966), 223–228. MR 192260
- Richard Askey, A transplantation theorem for Jacobi coefficients, Pacific J. Math. 21 (1967), 393–404. MR 217509
- Glen Baxter, A convergence equivalence related to polynomials orthogonal on the unit circle, Trans. Amer. Math. Soc. 99 (1961), 471–487. MR 126126, DOI 10.1090/S0002-9947-1961-0126126-8 10. K. K. Chen, On the Cèsaro-summability of the Laplace’s series of hyperspherical functions, Sci. Rep. Tôhoku Imp. Univ. Ser. 1, 17 (1928), 1073-1089. 11. A. Erdélyi et. al., Bateman Manuscript Project, H.T.F. vol. 2, New York, 1953.
- A. Erdélyi, Asymptotic solutions of differential equations with transition points or singularities, J. Mathematical Phys. 1 (1960), 16–26. MR 111915, DOI 10.1063/1.1703631 13. D. Ernst, Über die Laguerre-transformation und ihre Umkehrung, unpublished Doctoral Dissertation, Aachen, 1965. 14. C. Ganser, Integrability theorems for ultraspherical series, Duke Math. J, (to appear).
- Hans Günzler, Verallgemeinerte Fourierreihen, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1962 (1962), 81–122 (German). MR 147846
- Douglas L. Guy, Hankel multiplier transformations and weighted $p$-norms, Trans. Amer. Math. Soc. 95 (1960), 137–189. MR 120506, DOI 10.1090/S0002-9947-1960-0120506-1 17. G. H. Hardy and J. E. Littlewood, Some new properties of Fourier coefficients, J. London Math. Soc. 6 (1931), 3-9.
- 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
- Carl S. Herz, On the mean inversion of Fourier and Hankel transforms, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 996–999. MR 63477, DOI 10.1073/pnas.40.10.996
- I. I. Hirschman, The decomposition of Walsh and Fourier series, Mem. Amer. Math. Soc. 15 (1955), 65. MR 72269
- Satoru Igari, On the decomposition theorems of Fourier transforms with weighted norms, Tohoku Math. J. (2) 15 (1963), 6–36. MR 146591, DOI 10.2748/tmj/1178243866 22. E. Kogbetliantz, Recherches sur la sommabilité des séries ultrasphériques par la méthode des moyennes arithmétiques, J. Math. Pures Appl. (3) 9 (1924), 107-187. 23. A. Kolmogoroff, Sur les fonctions harmonique conjugées et les séries de Fourier, Fund. Math. 7 (1925), 24-29.
- Lee Lorch, The Lebesgue constants for Jacobi series. I, Proc. Amer. Math. Soc. 10 (1959), 756–761. MR 109981, DOI 10.1090/S0002-9939-1959-0109981-3
- B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17–92. MR 199636, DOI 10.1090/S0002-9947-1965-0199636-9
- Seymour V. Parter, On the existence and uniqueness of symmetric axially symmetric potentials, Arch. Rational Mech. Anal. 20 (1965), 279–286. MR 190358, DOI 10.1007/BF00253137
- Harry Pollard, The mean convergence of orthogonal series of polynomials, Proc. Nat. Acad. Sci. U.S.A. 32 (1946), 8–10. MR 14499, DOI 10.1073/pnas.32.1.8
- 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
- Marcel Riesz, Sur les fonctions conjuguées, Math. Z. 27 (1928), no. 1, 218–244 (French). MR 1544909, DOI 10.1007/BF01171098
- Elias M. Stein, Localization and summability of multiple Fourier series, Acta Math. 100 (1958), 93–147. MR 105592, DOI 10.1007/BF02559603
- Gen-ichirô Sunouchi, Discrete analogue of a theorem of Littlewood-Paley, Tohoku Math. J. (2) 13 (1961), 295–319. MR 159190, DOI 10.2748/tmj/1178244305 34. G. Szegö, Asymptotische Entwicklungen der Jacobischen Polynome, Schriften der Königsberger Gelehrten Gesellschaft, naturwissenschaftliche Klasse 10 (1933), 35-112.
- Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, R.I., 1959. Revised ed. MR 0106295
- 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
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
Additional Information
- Journal: Bull. Amer. Math. Soc. 72 (1966), 808-823
- DOI: https://doi.org/10.1090/S0002-9904-1966-11568-9
- MathSciNet review: 0198114