Abstract
In this paper we introduce a class of one dimensional non-centered minimal operator \({\widetilde{m}}_\Phi \) associated to a function \(\Phi \), which covers the usual minimal operator. We establish the boundedness of \({\widetilde{m}}_\Phi :\textrm{BV}(\mathbb {R})\rightarrow \textrm{BV}(\mathbb {R})\) under a more restrictive condition on \(\Phi \). Here \(\textrm{BV}(\mathbb {R})\) is the set of functions of bounded variation defined on \(\mathbb {R}\). In the discrete setting, we prove the discrete minimal operator is bounded and continuous from \(\textrm{BV}(\mathbb {Z})\) to itself under a more restrictive condition on \(\Phi \).
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The second author was supported partly by the Natural Science Foundation of Shandong Province (Grant No. ZR2023MA022).
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The second author was supported partly by the Natural Science Foundation of Shandong Province (Grant No. ZR2023MA022) and National Natural Science Foundation of China (12326371).
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Li, J., Liu, F. The Minimal Function of a BV Function. Results Math 79, 101 (2024). https://doi.org/10.1007/s00025-024-02124-4
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DOI: https://doi.org/10.1007/s00025-024-02124-4