Lévy processes and Fourier multipliers

Journal of Functional Analysis

Volumn 250, Issue 1, 2007, Pages 197-213

  Bañuelos, Rodrigo ^a   Bogdan, Krzysztof ^b  

^a PURDUE UNIVERSITY   (United States)

^b WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Fourier multiplier; Martingale transform; Process with independent increments; Singular integral

Indexed keywords

EID: 34547098114     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2007.05.013     Document Type: Article

References (20)

1. p-bounds for the Beurling-Ahlfors transform, Trans. Amer. Math. Soc., in press
2. Bañuelos R., and Méndez-Hernández P.J. Space-time Brownian motion and the Beurling-Ahlfors transform. Indiana Univ. Math. J. 52 4 (2003) 981-990
3. Bañuelos R., and Wang G. Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms. Duke Math. J. 80 3 (1995) 575-600
4. Burkholder D.L. Boundary value problems and sharp inequalities for martingale transforms. Ann. Probab. 12 3 (1984) 647-702
5. Burkholder D.L. Sharp inequalities for martingales and stochastic integrals. Astérisque 157-158 (1988) 75-94
6. Calderón A.-P., and Zygmund A. Singular integral operators and differential equations. Amer. J. Math. 79 (1957) 901-921
7. Dellacherie C., and Meyer P.-A. Probabilities and Potential, B. Theory of Martingales. North-Holland Math. Stud. vol. 72 (1982), North-Holland, Amsterdam Translated from the French by J.P. Wilson
8. p (C). Indiana Univ. Math. J. 54 4 (2005) 971-995
9. Farkas W., Jacob N., and Schilling R.L. Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces. Dissertationes Math. (Rozprawy Mat.) 393 (2001) 62
10. Gundy R.F., and Varopoulos N.T. Les transformations de Riesz et les intégrales stochastiques. C. R. Acad. Sci. Paris Sér. A-B 289 1 (1979) A13-A16
11. Iwaniec T. Extremal inequalities in Sobolev spaces and quasiconformal mappings. Z. Anal. Anwendungen 1 6 (1982) 1-16
12. Iwaniec T., and Martin G. Riesz transforms and related singular integrals. J. Reine Angew. Math. 473 (1996) 25-57
13. p potential theory for sub-Markovian semigroups: Kernels and capacities. Acta Math. Sinica 22 4 (2006) 1227-1250
14. Lehto O. Remarks on the integrability of the derivatives of quasiconformal mappings. Ann. Acad. Sci. Fenn. Ser. A I 371 8 (1965)
15. McConnell T.R. On Fourier multiplier transformations of Banach-valued functions. Trans. Amer. Math. Soc. 285 2 (1984) 739-757
16. Protter P.E. Stochastic Integration and Differential Equations. Stoch. Model. Appl. Probab. second ed. vol. 21 (2004), Springer-Verlag, Berlin
17. Sato K.-I. Lévy Processes and Infinitely Divisible Distributions. Cambridge Stud. Adv. Math. vol. 68 (1999), Cambridge Univ. Press, Cambridge Translated from the 1990 Japanese original, revised by the author
18. Stein E.M. Singular Integrals and Differentiability Properties of Functions. Princeton Math. Ser. vol. 30 (1970), Princeton Univ. Press, Princeton, NJ
19. Volberg A., and Nazarov F. Heat extension of the Beurling operator and estimates for its norm. Algebra i Analiz 15 4 (2003) 142-158
20. Wang G. Differential subordination and strong differential subordination for continuous-time martingales and related sharp inequalities. Ann. Probab. 23 2 (1995) 522-551