Space-Time Brownian Motion and the Beurling-Ahlfors Transform

Indiana University Mathematics Journal

Volumn 52, Issue 4, 2003, Pages 981-990

  Banuelos R ^a   Mendez Hernandez P J ^b  

^a PURDUE UNIVERSITY   (United States)

^b UNIVERSITY OF UTAH   (United States)

Author keywords

Beurling Ahlforms operator; Martingales; Singular integrals; Space time Brownian motion

Indexed keywords

EID: 0142200437     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2003.52.2218     Document Type: Article

References (14)

1. A. BAERNSTEIN II and S.J. MONTGOMERY-SMITH, Some conjectures about integral means of ∂f and ∂̄f, Acta Universitatis Upsaliensis 64 (1999) (Festschrift for M. Essén, ed. by C. Kiselman), 92-109.
2. R. BAÑUELOS, Martingale transforms and related singular integrals, Trans. Amer. Math. Soc. 293 (1986), 547-563.
3. R. BAÑUELOS and G. WANG, Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms, Duke Math. Journal 80 (1995), 575-600.
4. D.L. BURKHOLDER, Sharp inequalities for martingales and stochastic integrals, Astérique 157-158 (1988) (Colloque Paul Lévy (Palaiseau, 1987)), 75-94.
5. _, A proof of Pelczy'nski's conjecture for the Haar system, Studia Math. 91 (1988), 79-83.
6. _, Differential subordination of harmonic functions and martingales, Harmonic Analysis and Partial Differential Equations (El Escorial, 1989), Lecture Notes in Math., vol. 1384, Springer-Verlag, 1989.
7. _, Martingales and Singular Integrals in Banach Spaces, Handbook on the Geometry of Banach Spaces (Edited by W.B. Johnson and J. Lindenstrauss, North-Holland, 2003.
8. R.F. GUNDY and N.TH. VAROPOULOS, Les transformations de Riesz et les intégrales stochastiques, C.R. Acad. Sci. Paris 989 (1979), A13-A16.
9. T. IWANIEC, Extremal inequalities in Sobolev spaces and quasiconformal mappings, Z. Anal. Anwendungen 6 (1982), 1-16.
10. T. IWANIEC and R. KOSECKI, Sharp estimates for complex potentials and quasiconformal mappings (preprint).
11. n (preprint).
12. P.A. MEYER, Démonstration probabiliste de certain inégalités de Littlewood-Paley, Seminaire de Probabilités X (Univ. Strasbourg, 1974/75), Lecture Notes in Math., vol. 511, Springer-Verlag, Berlin, 1982.
13. F. NAZAROV and A. VOLBERG, Heating of the Beurling operator and the estimates of its norm, St. Petersburg Math. J. (to appear).
14. E. STEIN, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, 1970.