Abstract
Classical Hardy’s inequalities are concerned with the Hardy operator and its adjoint, the Bellman operator. Hausdorff operators in their various forms are natural generalizations of these two operators. Recently, the scheme used by Bradley for Hardy’s inequalities with general weights has been adjusted to the Hausdorff setting. For the Hardy and Bellman operators, the obtained necessary and sufficient conditions coincide and reduce to the classical ones. However, in this paper, we show that sufficient conditions for Hausdorff operators can be simplified. These are used for purely power weights, while for more general weights, only general necessary conditions are applied. The corresponding results are supplemented by examples.
| Original language | English |
|---|---|
| Pages (from-to) | 435-447 |
| Number of pages | 13 |
| Journal | Journal of Mathematical Sciences (United States) |
| Volume | 266 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2022 |
Bibliographical note
Publisher Copyright:© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
Funding
This work was mainly done during the author’s visit to the Basque Center for Applied Mathematics, Bilbao, Spain. This visit became possible due to efforts and hospitality of Carlos Pérez Moreno and Luz Roncal. Discussions with Luz Roncal were extremely important for making the ends meet in massive calculations and arguments.
Keywords
- Broken power weight
- Hardy inequality
- Hausdorff operator
- Power weight