Oscillation and variation for the hilbert transform

Duke Mathematical Journal

Volumn 105, Issue 1, 2000, Pages 59-83

  Campbell, James T ^a   Jones, Roger L ^b   Reinhold, Karin ^c   Wierdl, Máté ^a  

^a University of Memphis   (United States)

^b DEPAUL UNIVERSITY   (United States)

^c STATE UNIVERSITY OF NEW YORK   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034666903     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-00-10513-3     Document Type: Article

References (9)

1. M. Akcoglu, R. L. Jones, and P. Schwartz, Variation in probability, ergodic theory and analysis, Illinois J. Math. 42 (1998), 154-177.
2. J. Bourgain, Pointwise ergodic theorems for arithmetic sets, Inst. Hautes Etudes Sci. Publ. Math. 69 (1989), 5-45.
3. R. Jones, Ergodic theory and connections with analysis and probability, New York J. Math. 3A (1997), 31-67, available from http://nyjm.albany.edu:8000/nyjm.html.
4. R. Jones, R. Kaufmann, J. Rosenblatt, and M. Wierdl, Oscillation in ergodic theory Ergodic Theory Dynam. Systems 18 (1998), 889-935.
5. R. Jones, I. Ostrovskii, and J. Rosenblatt, Square functions in ergodic theory, Ergodic Theory Dynam. Systems 16 (1996), 267-305.
6. R. Jones, J. Rosenblatt, and M. Wierdl, Oscillation in ergodic theory: Higher dimensional results, preprint, http://moni.msci.memphis.edu/mw/high-final.pdf.
7. J. Qian, The p-variation of partial sum processes and the empirical process, Ann. Probab. 26 (1998), 1370-1383.
8. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Math. Ser. 30, Princeton Univ. Press, Princeton, 1970.
9. A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Pure Appl. Math. 123, Academic Press, Orlando, 1986.