Persons
Mgr. Martin Křepela, Ph.D.
All publications
A Weak-Type Expression of the Orlicz Modular
- Authors: Mgr. Martin Křepela, Ph.D., RNDr. Zdeněk Mihula, Ph.D., Soria, J.
- Publication: MEDITERRANEAN JOURNAL OF MATHEMATICS. 2023, 20(3), 1-8. ISSN 1660-5446.
- Year: 2023
- DOI: 10.1007/s00009-023-02315-3
- Link: https://doi.org/10.1007/s00009-023-02315-3
- Department: Department of Mathematics
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Annotation:
An equivalent expression of Orlicz modulars in terms of measure of level sets of difference quotients is established. The result in a sense complements the famous Maz'ya-Shaposhnikova formula for the fractional Gagliardo-Slobodeckij seminorm and its recent extension to the setting of Orlicz functions.
Discretization and antidiscretization of Lorentz norms with no restrictions on weights
- Authors: Mgr. Martin Křepela, Ph.D., RNDr. Zdeněk Mihula, Ph.D., Turcinova, H.
- Publication: Revista Matemática Complutense. 2022, 35(2), 615-648. ISSN 1139-1138.
- Year: 2022
- DOI: 10.1007/s13163-021-00399-7
- Link: https://doi.org/10.1007/s13163-021-00399-7
- Department: Department of Mathematics
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Annotation:
We improve the discretization technique for weighted Lorentz norms by eliminating all "non-degeneracy" restrictions on the involved weights. We use the new method to provide equivalent estimates on the optimal constant C such that the inequality
Lorentz and Gale-Ryser theorems on general measure spaces
- Authors: Boza, S., Mgr. Martin Křepela, Ph.D., Soria, J.
- Publication: Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 2022, 152(4), 857-878. ISSN 0308-2105.
- Year: 2022
- DOI: 10.1017/prm.2021.37
- Link: https://doi.org/10.1017/prm.2021.37
- Department: Department of Mathematics
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Annotation:
Based on the Gale-Ryser theorem [2, 6], for the existence of suitable (0, 1)-matrices for different partitions of a natural number, we revisit the classical result of Lorentz [4] regarding the characterization of a plane measurable set, in terms of its cross-sections, and extend it to general measure spaces.