On Necessary Multiplier Conditions for Laguerre Expansions

Gasper, George ; Trebels, Walter

Canadian journal of mathematics, Tome 43 (1991) no. 6, pp. 1228-1242

Résumé

Necessary multiplier conditions for Laguerre expansions are derived and discussed within the framework of weighted Lebesgue spaces.

Détail

DOI : 10.4153/CJM-1991-070-9

Mots-clés : 33A65, 42A45, 42C10

Bibliographie

[1] 1. Askey, R., Dual equations and classical orthogonal polynomials, J. Math. Anal. Appl. 24(1968), 677–685. Google Scholar

[2] 2. Askey, R. and Wainger, S., Mean convergence of expansions in Laguerre andHermite series, Amer. J. Math. 87(1965), 695–708. Google Scholar

[3] 3. Dhigosz, J., LP -multipliers for the Laguerre expansions, Colloq. Math. 54(1987), 285–293. Google Scholar

[4] 4. Erdelyi, A. et al., Higher transcendental functions, vols. I & II. McGraw Hill, New York, 1953. Google Scholar

[5] 5. Gasper, G. and Trebels, W., A characterization of localized Bessel potential spaces and applications to Jacobi andHankel multipliers, Studia Math. 65(1979), 243–278. Google Scholar

[6] 6. Gasper, G. and Trebels, W., A Hausdorff-Young inequality and necessary multiplier conditions for Jacobi expansions, Acta Sci. Math. 42(1980), 247–255. Google Scholar

[7] 7. Gasper, G. and Trebels, W., Necessary conditions for Hankel multipliers, Indiana Univ. Math. J. 31(1982), 403–414. Google Scholar

[8] 8. Görlich, E. and Markett, C., Estimates for the norm of the Laguerre translation operator, Numer. Funct. Anal. Optim. 1(1979), 203–222. Google Scholar

[9] 9. Görlich, E. and Markett, C., A convolution structure for Laguerre series, Indag. Math. 44(1982), 161–171. Google Scholar

[10] 10. Kanjin, Y., A transplantation theorem for Laguerre series, to appear. Google Scholar

[11] 11. Luke, Y.L., The special functions and their approximations, vols. I & II. Academic Press, New York, 1969. Google Scholar

[12] 12. Markett, C., Norm estimates for Cesàro means of Laguerre expansions, in Approximation and Function Spaces (Gdansk 1979), pp. 419–435. North Holland, Amsterdam, 1981. Google Scholar

[13] 13. Markett, C., Nikolskii-Type inequalities for Laguerre andHermite expansions, Coll. Math. Soc. János Bolyai, Budapest 35(1980), pp. 811–834. Google Scholar

[14] 14. Markett, C., Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter, Anal. Math. 8(1982), 19–37. Google Scholar

[15] 15. Muckenhoupt, B., Poisson integrals for Hermite and Laguerre expansions, Trans. Amer. Math. Soc. 139(1969), 231–242. Google Scholar

[16] 16. Muckenhoupt, B., Mean convergence of Hermite and Laguerre series II, Trans. Amer. Math. Soc. 147(1970), 433–460. Google Scholar

[17] 17. Poiani, E.L., Mean Cesàro summability of Laguerre and Hermite series, Trans. Amer. Math. Soc. 173(1972), 1–31. Google Scholar

[18] 18. Stein, E.M. and Weiss, G., Interpolation of operators with change of measures, Trans. Amer. Math. Soc. 87(1958), 159–172. Google Scholar

[19] 19. Szegö, G., Orthogonal polynomials. 4th éd., Amer. Math. Soc. Colloq. Publ. 23, Providence, R.I. 1975. Google Scholar

[20] 20. Trebels, W., Multipliers for (C, a)-bounded Fourier expansions in Banach spaces and approximation theory. Springer Lecture Notes in Math. 329, Springer-Verlag, Berlin 1973. Google Scholar

[21] 21. Tricomi, F.G., Vorlesungen über Orthogonalreihen. Springer-Verlag, 1970. Google Scholar

[22] 22. Zeller, K. und Beekmann, W., Theorie der Limitierungsverfahren. 2nd éd., Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 15, Springer-Verlag, Berlin 1970. Google Scholar