$H^ p$ estimates for bi-invariant operators on compact Lie groups
HTML articles powered by AMS MathViewer
- by Da Shan Fan and Zeng Fu Xu PDF
- Proc. Amer. Math. Soc. 122 (1994), 437-447 Request permission
Abstract:
The main purpose of this paper is to extend to compact Lie groups a Hรถrmander multiplier theorem concerning translation invariant operators on Hardy spaces ${H^p},0 < p \leq 1$.References
-
B. Blank and D. Fan, ${H^p}$ spaces on compact Lie groups (submitted).
- A. Baernstein II and E. T. Sawyer, Embedding and multiplier theorems for $H^P(\textbf {R}^n)$, Mem. Amer. Math. Soc. 53 (1985), no.ย 318, iv+82. MR 776176, DOI 10.1090/memo/0318
- Walter R. Bloom and Zeng Fu Xu, Approximation of $H^p$-functions by Bochner-Riesz means on compact Lie groups, Math. Z. 216 (1994), no.ย 1, 131โ145. MR 1273469, DOI 10.1007/BF02572312
- Jean-Louis Clerc, Bochner-Riesz means of $H^p$ functions $(0<p<1)$ on compact Lie groups, Noncommutative harmonic analysis and Lie groups (Marseille-Luminy, 1985) Lecture Notes in Math., vol. 1243, Springer, Berlin, 1987, pp.ย 86โ107. MR 897539, DOI 10.1007/BFb0073019
- A.-P. Calderรณn and A. Torchinsky, Parabolic maximal functions associated with a distribution. II, Advances in Math. 24 (1977), no.ย 2, 101โ171. MR 450888, DOI 10.1016/S0001-8708(77)80016-9 L. Colzani Hardy space on sphere, Ph.D. Thesis, Washington Univ., St. Louis, 1982.
- Ronald R. Coifman and Guido Weiss, Thรฉorรจmes sur les multiplicateurs de Fourier sur $\textrm {SU}(2)$ et $\sum _{2}$, C. R. Acad. Sci. Paris Sรฉr. A-B 271 (1970), A928โA930 (French). MR 271274
- Ronald R. Coifman and Guido Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no.ย 4, 569โ645. MR 447954, DOI 10.1090/S0002-9904-1977-14325-5
- C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), no.ย 3-4, 137โ193. MR 447953, DOI 10.1007/BF02392215
- Robert H. Latter, A characterization of $H^{p}(\textbf {R}^{n})$ in terms of atoms, Studia Math. 62 (1978), no.ย 1, 93โ101. MR 482111, DOI 10.4064/sm-62-1-93-101
- R. A. Mayer, Fourier series of differentiable functions on $\textrm {SU}(2)$, Duke Math. J. 34 (1967), 549โ554. MR 249541, DOI 10.1215/S0012-7094-67-03459-X
- Elias M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory. , Annals of Mathematics Studies, No. 63, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. MR 0252961
- Norman J. Weiss, $L^{P}$ estimates for bi-invariant operators on compact Lie groups, Amer. J. Math. 94 (1972), 103โ118. MR 296217, DOI 10.2307/2373596
- Zeng Fu Xu, The generalized Abel means of $H^p$ functions $(0<p\leq 1)$ on compact Lie groups, Chinese Ann. Math. Ser. A 13 (1992), no.ย 1, 101โ110 (Chinese). MR 1166864
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 437-447
- MSC: Primary 43A22; Secondary 22E30
- DOI: https://doi.org/10.1090/S0002-9939-1994-1198454-6
- MathSciNet review: 1198454