Abstract
These transformations are called the Hardy and Bellman transformations, respectively. In this paper, we generalize these results in three directions: we consider Fourier series with respect to regular orthonormal systems [3] (including all trigonometric and multiplicative systems with bounded generators); a generalization of the Hardy and Bellman transformations is introduced; the boundedness of generalized transformations in anisotropic Lorentz spaces [3] is studied.
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