References
K. F. Andersen and H. P. Heinig, Weighted norm inequalities for certain integral operators,SIAM J. Math. Anal.,14 (1983), 834–844.
R. Askey and J. Fitch, Integral representations for Jacobi polynomials and some applications,J. Math. Anal. Appl.,26 (1969), 411–437.
K. de Leeuw, OnL p multipliers,Ann. of Math. 81 (1965), 364–379.
G. Gasper, K. Stempak, and W. Trebels, Fractional integration for Laguerre expansions,Methods and Applications of Analysis (to appear).
G. Gasper and W. Trebels, A characterization of localized Bessel potential spaces and applications to Jacobi and Hankel multipliers,Studia Math.,65 (1979), 243–278.
G. Gasper and W. Trebels, On necessary multiplier conditions for Laguerre expansions,Canad. J. Math.,43 (1991), 1228–1242.
E. Görlich and C. Markett, A convolution structure for Laguerre series,Indag. Math.,44 (1982), 161–171.
G. H. Hardy, J. E. Littlewood, and G. Polya,Inequalities, Cambridge University Press (Cambridge, 1964).
Y. Kanjin, A transplantation theorem for Laguerre series,Tohoku Math. J. 43 (1991), 537–555.
C. Markett, Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter,Anal. Math.,8 (1982), 19–37.
B. Muckenhoupt, Hardy's inequality with weights,Studia Math.,44 (1972), 31–38.
B. Muckenhoupt, Transplantation theorems and multiplier theorems for Jacobi series,Mem. Amer. Math. Soc.,64 (1986), no. 356.
B. Muckenhoupt, R. L. Wheeden, and Wo-Sang Young,L 2 multipliers with power weights,Adv. in Math.,49 (1983), 170–216.
K. Stempak and W. Trebels, On weighted transplantation and multipliers for Laguerre expansions,Math. Ann.,300 (1994), 203–219.
G. Szegö,Orthogonal Polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ. 23 (Providence, R.I., 1975).
S. Thangavelu, Transplantation, summability and multipliers for multiple Laguerre expansions,Tohoku Math. J.,44 (1992), 279–298.
M. Zafran, Interpolation of multiplier spaces,Amer. J. Math.,105 (1983), 1405–1416.
Author information
Authors and Affiliations
Additional information
Dedicated to Professor Károly Tandori on the occasion of his 70th birthday
The work of this author was supported in part by the National Science Foundation under grant DMS-9103177.
Rights and permissions
About this article
Cite this article
Gasper, G., Trebels, W. On a restriction problem of de Leeuw type for Laguerre multipliers. Acta Math Hung 68, 135–149 (1995). https://doi.org/10.1007/BF01874440
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01874440