Good modulating sequences for the ergodic Hilbert transform

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

This article investigates classes of bounded sequences of complex numbers that are universally good for the ergodic Hilbert transform in Lp-spaces, 2 \leq p \leq \infty. The class of bounded Besicovitch sequences satisfying a rate condition is among such sequence classes.

Anahtar Kelimeler:

Hilbert transform, bounded Besicovitch sequences, modulating sequences

Good modulating sequences for the ergodic Hilbert transform

Keywords:

Hilbert transform, bounded Besicovitch sequences, modulating sequences,

PDF

___

Bellow A, Losert V. The weighted pointwise ergodic theorem and the individual ergodic theorem along subsequences. T Am Math Soc 1985; 288: 307–345.
Brunel A, Keane M. Ergodic theorems for operator sequences. Z Wahrscheinlichkeitsrechnung Verw Gebiete 1969; 12: 231–240.
Campbell J, Petersen K. The spectral measure and Hilbert transform of a measure-preserving transformation. T Am Math Soc 1989; 313: 121–129.
Cotlar M. A unified theory of of Hilbert transforms and ergodic theorem. Rev Mat Cuyana 1955; 1: 105–167.
C¸ ¨omez D. Existence of discrete ergodic singular transforms for admissible processes. Colloq Math 2008; 112: 335– 3
C¸ ¨omez D. The modulated ergodic Hilbert transform. Discrete Cont Dyn S Series S 2009; 2: 325–336.
Jajte R. On the existence of the ergodic Hilbert transform. Ann Probab 1987; 15: 831–835.
Kahane JP. Sur les coefficients de Fourier-Bohr. Stud Math 1961; 21: 103106 (in French).
Lacey M, Terwilleger E. A Wiener-Wintner theorem for the Hilbert transform. Ark Mat 2008; 46: 315–336.
Petersen K. Another proof of the existence of the ergodic Hilbert transform. P Am Math Soc 1983; 88: 39–43.
Sato R. A remark on the ergodic Hilbert transform. Math. J Okayama Univ 1986; 28: 159–163.
Zygmund A. Trigonometric Series. Cambridge, UK: Cambridge University Press, 1959.