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Endpoint Regularity of the Discrete Multisublinear Fractional Maximal Operators

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Abstract

We study the endpoint regularity of the one-dimensional discrete multisublinear fractional maximal operators, both in the centered and uncentered versions. Some new variation inequalities will be proved for the above operators acting on the vector-valued function \(\mathbf {f}=(f_1, \ldots ,f_m)\) with each \(f_j\) belonging to \(\mathrm{BV}({\mathbb {Z}})\) or \(\ell ^1({\mathbb {Z}})\), where \(\mathrm{BV}({\mathbb {Z}})\) denotes the set of functions of bounded variation defined on \({\mathbb {Z}}\). In addition, it was also shown that the above operators are bounded and continuous from \(\ell ^1({\mathbb {Z}})\times \cdots \times \ell ^1({\mathbb {Z}})\) to \(\mathrm{BV}({\mathbb {Z}})\). The above results represent significant and natural extensions of what was known previously.

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Acknowledgements

The author want to express her sincerely thanks to the referees for their valuable remarks and suggestions, which made this paper more readable.

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  1. College of Electronic and Information Engineering, Shandong University of Science and Technology, Qingdao, 266590, Shandong, People’s Republic of China

    Xiao Zhang

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  1. Xiao Zhang
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Zhang, X. Endpoint Regularity of the Discrete Multisublinear Fractional Maximal Operators. Results Math 76, 77 (2021). https://doi.org/10.1007/s00025-021-01387-5

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