PreprintCC BY 4.0arXiv
On sharp constants for infinitely many equivalent norms on Cesàro function spaces
Abstract
Recent years have seen significant interest in finding equivalent norms on Cesàro function spaces together with their optimal equivalence constants. In this work, we continue this line of research by deriving sharp two-sided inequalities relating the Lp-norms of 𝒞m f and 𝒞n f, where 𝒞k is the generalized Cesàro operator of order k ∈ ℕ acting on non-negative measurable functions f on (0,∞). A parallel study is also conducted for the corresponding adjoint operators.
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BibTeX
@misc{said2026sharp,
title = {{On sharp constants for infinitely many equivalent norms on Cesàro function spaces}},
author = {Achraf Ben Said and Miguel Monsalve-López},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22964},
eprint = {2609.22964},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22964},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On sharp constants for infinitely many equivalent norms on Cesàro function spaces
AU - Achraf Ben Said
AU - Miguel Monsalve-López
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.22964
UR - https://arxiv.org/abs/2609.22964
AB - Recent years have seen significant interest in finding equivalent norms on Cesàro function spaces together with their optimal equivalence constants. In this work, we continue this line of research by deriving sharp two-sided inequalities relating the L^p-norms of 𝒞_m f and 𝒞_n f, where 𝒞_k is the generalized Cesàro operator of order k ∈ ℕ acting on non-negative measurable functions f on (0,∞). A parallel study is also conducted for the corresponding adjoint operators.
ER -