Abstract
The classical Hardy–Littlewood result states that ‖|⋅|1−2/p|fˆ|‖p≲‖f‖p for 1<p⩽2. The similar inequality for orthonormal Fourier series has been obtained by Paley. We extend these results for any p>1 considering different integral averages of f in the left-hand side of the estimates.
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