Abstract
В работе с использова нием теоремыА p -алгеб ры сначала доказываетс я одна теорема трансференции, прина длежащая Койфману и В ейсу. Затем эти же соображения пр именяются для исследования цен тральных мультиплик аторов рядов Фурье на компактных п олупростых группах Ли иAd-инвариа нтных мультипликато ров преобразований Фурь е на алгебрах Ли таких групп.
Bibliography
J.-L. Clerc, Sommes de Riesz et multiplicateurs sur un groupe de Lie compact,Annales Inst. Fourier, Grenoble,24, 1 (1974), 149–172.
R. R.Coifman and G.Weiss,Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math.,242 (1971).
—, Operators associated with representations of amenable groups, singular integrals induced by ergodic flows, the rotation method and multipliers,Studia Math.,47 (1973), 285–303.
—, Operators transferred by representations of an amenable group,Proc. Symp. Pure Math.,26 (1973), 369–372.
—, Central multiplier theorems for compact Lie groups,Bull. A. M. S.,80 (1974), 124–126.
- and -,Transference methods in analysis, C. B. M. S. Lecture Notes31 (1977).
M. Cowling, Some applications of Grothendieck's theory of topological tensor products in harmonic analysis,Math. Ann.,232 (1978), 273–285.
H.Dappa,Quasiradiale Fouriermultiplikatoren, Dissertation (Darmstadt 1982).
K. De Leeuw, OnL p multipliers,Annals Math.,81 (1965), 364–379.
R. E. Edwards andG. I. Gaudry, Littlewood-Paley and multiplier theory,Ergebnisse Math. 90, Springer (Berlin, Heidelberg, New York, 1977).
A. El Kohen, Maximal operators on hyperboloids,J. Operator Theory,3 (1980), 41–56.
P.Eymard,Algèbres Ap et convoluteurs de Lp, Sem. Bourbaki, n∘.367, November 1969.
R. O. Gandulfo,Multiplier operators for expansions in spherical harmonics and ultraspherical polynomials, Dissertation (Washington University, St. Louis 1975).
—, Transference results for multiplier operators,Bull. A. M. S.,82 (1976), 734–736.
- and J. A.Tirao,Multiplier transformations of functions on compact twopoint homogeneous spaces, Trabalhos de Matematica, n∘. 126, September 1977.
S. Helgason,Differential geometry and symmetric spaces, Academic Press (New York, London, 1962).
C. Herz, Le rapport entre les algèbresA p d'un groupe et d'un sousgroupe,C. R. Acad. Sci. Paris, A 271 (1970), 244–246.
—, The theory ofp-spaces with an application to convolution operators,Trans. A. M. S.,154 (1971), 69–82.
—, Harmonic synthesis for subgroups,Annales Inst. Fourier, Grenoble,23, 3 (1973), 91–123.
E. Hewitt andK. A. Ross,Abstract harmonic analysis. I & II, Springer (Berlin, Heidelberg, New York, 1963 & 1970).
L. Hörmander, Estimates for translation invariant operators inL P spaces,Acta Math.,104 (1960), 93–140.
S. Igari andS. Kuratsubo, A sufficient condition forL p-multipliers,Pacific J. Math.,38, 1 (1971), 85–88.
W. Littman, Multipliers inL p and interpolation,Bull. A. M. S.,71 (1965), 764–766.
G. Mauceri, Zonal multipliers on the Heisenberg group,Pacific J. Math.,95, 1 (1981), 143–159.
J.Peetre, New thoughts on Besov spaces,Duke Univ. Math. Series,1 (Durham, N. C, 1976).
D. L. Ragozin, Rotation invariant measure algebras on Euclidean spaces,Indiana Univ. Math. J.,23 (1974), 1139–1154.
—, Zonal measure algebras on isotropy irreducible homogeneous spaces,J. Funct. Anal.,17 (1974), 355–376.
S. G. Roberts,A p spaces and asymmetry of p operator norms for convolution operators, M. Sc. Thesis (Flinders University, South Aust., March 1982).
L.Schwartz, Sur les multiplicateurs deℱ, Kungl. Fysiografiska Sällskapets i Lund Förhandlingar22, no. 21 (1953).
R. J. Stanton, Mean convergence of Fourier series on compact Lie groups,Trans. A. M. S.,218 (1976), 61–87.
— andP. A. Tomas, Expansions for spherical functions on noncompact symmetric spaces,Acta Math.,140 (1978), 251–276.
E. M. Stein andG. Weiss,Introduction to Fourier analysis on Euclidean spaces, Univ. Press (Princeton, N. J., 1971).
R. S. Strichartz, Multiplier transformations on compact Lie groups and algebras,Trans. A. M. S.,193 (1974), 99–110.
—, Bochner identities for Fourier transforms,Trans. A. M. S.,228 (1977), 307–327.
V. S. Varadarajan,Lie groups, Lie algebras, and their representations, Prentice-Hall, Inc. (Englewood Cliffs, N. J., 1974).
L. Vretare, OnL p multipliers on a compact Lie group,Math. Scand.,35 (1974), 49–55.
N. J. Weiss,L p estimates for bi-invariant operators on compact Lie groups,Amer. J. Math.,94 (1972), 103–118.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Meaney, C. Transferring estimates for zonal convolution operators. Analysis Mathematica 15, 175–193 (1989). https://doi.org/10.1007/BF02020766
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02020766