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arXiv · 2407.15726

Classical discrete operators on variable $\ell^{p(\cdot)}(\mathbb{Z})$ spaces

Pablo Rocha
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Abstract

We show, by applying discrete weighted norm inequalities and the Rubio de Francia algorithm, that the discrete Hilbert transform and discrete Riesz potential are bounded on variable $\ell^{p(\cdot)}(\mathbb{Z})$ spaces whenever the discrete Hardy-Littlewood maximal is bounded on $\ell^{p'(\cdot)}(\mathbb{Z})$. We also obtain vector-valued inequalities for the discrete fractional maximal operator.

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Pablo Rocha. 2024-07-22. Classical discrete operators on variable $\ell^{p(\cdot)}(\mathbb{Z})$ spaces. https://arxiv.org/abs/2407.15726

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