Multipliers on weighted $L_ p$-spaces over locally compact Vilenkin groups
HTML articles powered by AMS MathViewer
- by C. W. Onneweer and T. S. Quek
- Proc. Amer. Math. Soc. 105 (1989), 622-631
- DOI: https://doi.org/10.1090/S0002-9939-1989-0937014-4
- PDF | Request permission
Abstract:
Let $G$ be a locally compact Vilenkin group. We prove a multiplier theorem for power-weighted ${L_p}(G)$-spaces which extends an earlier result of this kind, due to Onneweer.References
- Richard J. Bagby and Douglas S. Kurtz, Covering lemmas and the sharp function, Proc. Amer. Math. Soc. 93 (1985), no. 2, 291–296. MR 770539, DOI 10.1090/S0002-9939-1985-0770539-X
- R. E. Edwards and G. I. Gaudry, Littlewood-Paley and multiplier theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 90, Springer-Verlag, Berlin-New York, 1977. MR 0618663, DOI 10.1007/978-3-642-66366-6
- José García-Cuerva and José L. Rubio de Francia, Weighted norm inequalities and related topics, North-Holland Mathematics Studies, vol. 116, North-Holland Publishing Co., Amsterdam, 1985. Notas de Matemática [Mathematical Notes], 104. MR 807149
- Toshiyuki Kitada, Multipliers on weighted Hardy spaces over certain totally disconnected groups, Internat. J. Math. Math. Sci. 11 (1988), no. 4, 665–674. MR 959446, DOI 10.1155/S016117128800081X
- Douglas S. Kurtz and Richard L. Wheeden, Results on weighted norm inequalities for multipliers, Trans. Amer. Math. Soc. 255 (1979), 343–362. MR 542885, DOI 10.1090/S0002-9947-1979-0542885-8
- C. W. Onneweer, Multipliers on weighted $L_p$-spaces over certain totally disconnected groups, Trans. Amer. Math. Soc. 288 (1985), no. 1, 347–362. MR 773064, DOI 10.1090/S0002-9947-1985-0773064-X
- Elias M. Stein, Interpolation of linear operators, Trans. Amer. Math. Soc. 83 (1956), 482–492. MR 82586, DOI 10.1090/S0002-9947-1956-0082586-0
- M. H. Taibleson, Fourier analysis on local fields, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1975. MR 0487295
Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 622-631
- MSC: Primary 43A22; Secondary 43A70, 46E99
- DOI: https://doi.org/10.1090/S0002-9939-1989-0937014-4
- MathSciNet review: 937014