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A concept of absolute continuity and its characterization in terms of convergence in variation |
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| Authors: | Laura Angeloni Gianluca Vinti |
| Affiliation: | 1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy;2. +39 3. 075 4. 585 5. 5025+39 6. 5024 |
| Abstract: | We study the notion of φ‐absolute continuity, providing several equivalent definitions, and we prove a characterization of the space of φ‐absolutely continuous functions in terms of convergence in variation for a family of Mellin integral operators in the multidimensional setting. |
| Keywords: | φ ‐absolute continuity multidimensional φ ‐variation Mellin operators convergence in variation 26A45 26A46 41A35 26B30 47G10 |