Invariant operators on function spaces on homogeneous trees

• Autorzy: Michael Cowling , Stefano Meda , Alberto G. Setti
• Języki publikacji: EN

Słowa kluczowe

EN

spherical functions; harmonic analysis; homogeneous trees

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 80
• Numer: 1
• Strony: 53-61

Daty

wydano

1999

otrzymano

1998-07-20

Twórcy

autor

Michael Cowling

• School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia

autor

Stefano Meda

• Dipartimento di Statistica, Università 'Bicocca', Edificio U7, II piano, viale Sarca 202, I-20100 Milano, Italy

autor

Alberto G. Setti

• Facoltà di Scienze, Università dell'Insubria-Polo di Como, via Lucini 3, I-22100 Como, Italy

Bibliografia

• [BL] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Grundlehren Math. Wiss. 223, Springer, New York, 1976.
• [CS] J.-L. Clerc and E. M. Stein, $L^p$ multipliers for noncompact symmetric spaces, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 3911-3912.
• [CGM] M. Cowling, S. Giulini and S. Meda, $L^p-L^q$ estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. I, Duke Math. J. 72 (1993), 109-150.
• M. Cowling, S. Meda and A. G. Setti, Estimates for functions of the Laplace operator on homogeneous trees, Trans. Amer. Math. Soc., to appear.
• M. Cowling, S. Meda and A. G. Setti, An overview of harmonic analysis on the group of isometries of a homogeneous tree, Exposition. Math. 16 (1998), 385-423.
• [FTN] A. Figà-Talamanca and C. Nebbia, Harmonic Analysis and Representa- tion Theory for Groups Acting on Homogeneous Trees, London Math. Soc. Lecture Note Ser. 162, Cambridge Univ. Press, Cambridge, 1991.
• [FTP] A. Figà-Talamanca and M. Picardello, Harmonic Analysis on Free Groups, Lecture Notes in Pure and Appl. Math. 87, Marcel Dekker, New York, 1983.
• [Hö] L. Hörmander, Estimates for translation invariant operators in $L^p$ spaces, Acta Math. 104 (1960), 93-140.
• [Lo] N. Lohoué, Estimations $L^p$ des coefficients de représentation et opérateurs de convolution, Adv. Math. 38 (1980), 178-221.
• [N] C. Nebbia, Groups of isometries of a tree and the Kunze-Stein phenomenon, Pacific J. Math. 133 (1988), 141-149.
• [Py] T. Pytlik, Radial convolutors on free groups, Studia Math. 78 (1984), 178-183.
• [RT] R. Rochberg and M. Taibleson, Factorization of the Green's operator and weak-type estimates for a random walk on a tree, Publ. Mat. 35 (1991), 187-207.