Abstract
The Paley-Wiener theorem states that the Hilbert transform of an integrable odd function, which is monotone on \(\mathbb{R}_{+}\), is integrable. In this paper we prove weighted analogs of this theorem for sequences and their discrete Hilbert transforms under the assumption of general monotonicity for an even/odd sequence.
Mathematics Subject Classification (2000). Primary 42A50, Secondary 40A99, 26A48, 44A15
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Liflyand, E. (2016). Weighted Estimates for the Discrete Hilbert Transform. In: Ruzhansky, M., Tikhonov, S. (eds) Methods of Fourier Analysis and Approximation Theory. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-27466-9_5
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DOI: https://doi.org/10.1007/978-3-319-27466-9_5
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