Riesz transforms on spheres

Mathematical Research Letters

Volumn 4, Issue 2-3, 1997, Pages 401-412

  Arcozzi, Nicola ^a   Li, Xinwei ^b  

^a CAMPUS BOX 1146 ^*  (Italy)

^b WASHINGTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031287209     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/mrl.1997.v4.n3.a9     Document Type: Article

References (27)

1. [A1] N. Arcozzi, Riesz transforms on compact Lie groups, spheres and Gauss space, preprint, 1997.
2. [A2] _, Strong (p, p) and weak (1, 1) inequalities for systems of conjugate harmonic functions in Euclidean domains, preprint, 1997.
3. 1 sur les sphéres, Sém. de Prob. XVIII, 197-218, Lecture Notes in Math., 1059, Springer, 1984.
4. [Bañ] R. Bañuelos, Martingale transforms and related singular integrals, Trans. Amer. Math. Soc. 293 (1986), 547-563.
5. [BW] R. Bañuelos and G. Wang, Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms, Duke Math. J., 80 (1995), 575-600.
6. [Be] A. Bennett, Probabilitistic square functions and a priori estimates, Trans. Amer. Math. Soc. 291, (1985), 159-166.
7. [Bu] D. L. Burkholder, Sharp inequalities for martingales and stochastic integrals, Astérisque 157-158 (1988), 75-94.
8. [CW1] R. Coifman and G. Weiss, Invariant systems of conjugate harmonic functions associated with compact Lie groups, Studia Math. 44 (1972), 301-308.
9. [CW2] _, Transference methods in analysis, CBMS Regional Conf. Ser. in Math. 31, 1977.
10. [DF] J. Duoandikoetxea and J. L. Rubio de Francia, Estimations indépendantes de la dimension pour les transformées de Riesz, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), 193-196.
11. [Es] M. Essén, A superharmonic proof of the M. Riesz conjugate function theorem, Ark. Math. 22 (1984), 241-249.
12. [IM] T. Iwaniec and G. Martin, Riesz transforms and related singular integrals, J. Reine Angew. Math., 473 (1996), 25-57.
13. [Ku] Ü. Kuran, n-Dimensional extensions of theorems on conjugate functions, Proc. London Math. Soc. (3) 15 (1965), 713-730.
14. [KV1] A. Korányi and S. Vági, Singular integrals in homogeneous spaces and some problems of classical analysis, Ann. Scuola Norm. Sup. Pisa (3) 25 (1971), 575-648.
15. [KV2] A. Korányi and S. Vági, Group theoretic remarks on Riesz systems on balls, Proc. Amer. Math. Soc. 85 (1982), 200-205.
16. [Le] D. Levine, Systems of singular integral operators on spheres, Trans. Amer. Math. Soc. 144 (1969), 493-522.
17. [Li] X. Li, Thesis, Washington University, 1996.
18. [Lin] A. Lindeman II, Martingales and the n-dimensional Beurling-Ahlfors transform, preprint, 1995.
19. [Me] P. Meyer, Démonstrations probabilistes des inégalités de Littlewood-Paley, Sém. de Prob. X, Lecture Notes in Math., 511, Springer, 1976.
20. [Pic] S. K. Pichorides, On the best values of the constants in the theorems of M. Riesz, Zygmund and Kolmogorov, Studia Math. 44 (1972), 165-179.
21. [Pis] G. Pisier, Riesz transforms: A simple Analytic proof of P.A. Meyer's Inequality, Sém. de Prob. XXII, Lecture Notes in Math., 1321, Springer, 1988.
22. n-1), Proc. Sympos. Pure Math., XXXV, 1 (1979), 289-294.
23. [St1] E. M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory, Ann. of Math. Stud., 63, Princeton Univ. Press, Princeton, N.J., 1970.
24. [St2] _, Singular integrals and differentiability properties of functions, Princeton Math. Ser., 30, Princeton University Press, Princeton, N.J., 1970.
25. n, for n → ∞, Bull. Amer. Math. Soc. 9 (1983), 71-73.
26. [St4] _, Three variations on the theme of maximal functions, Recent Progress in Fourier Analysis, 229-244, I. Peral and J.-L. Rubio de Francia (Editors), North-Holland Math. Stud., 111, North-Holland 1985.
27. [SW] E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Math. Ser., 32, Princeton University Press, Princeton, N.J., 1971.