© 2018 Elsevier Inc. We obtain new conditions on periodic integrable functions so that their transformed Fourier series belong to Lp. This improves the classical Hardy and Bellman results. A counterpart for the Fourier transforms is also established. Our main tool is a new extension of the Hausdorff–Young–Paley inequality for Fourier transforms.
- Fourier coefficients/transforms
- Hardy and Hardy–Cesàro averages
- Hardy–Littlewood theorem
- Hausdorff–Young–Paley inequality