A class of fractal Hilbert-type inequalities obtained via Cantor-type spherical coordinates
• D. Baleanu,
• Mario Krnić,
• Predrag Vukovic
D. Baleanu
Institute of Space Science
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Mario Krnić
University of Zagreb Faculty of Electrical Engineering and Computing
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Predrag Vukovic
University of Zagreb Faculty of Teacher Education
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## Abstract

We present a class of higher-dimensional Hilbert-type inequalities on a fractal set $(\mathbb{R}_+^{\alpha n})^{k}$. The crucial step in establishing our results are higher-dimensional spherical coordinates on a fractal space. Further, we impose the corresponding conditions under which the constants appearing in the established Hilbert-type inequalities are the best possible. As an application, our results are compared with the previous results known from the literature.

#### Peer review status:Published

14 Oct 2020Submitted to Mathematical Methods in the Applied Sciences
19 Oct 2020Assigned to Editor
19 Oct 2020Submission Checks Completed
04 Nov 2020Reviewer(s) Assigned
04 Nov 2020Review(s) Completed, Editorial Evaluation Pending
22 Dec 2020Editorial Decision: Accept
10 Feb 2021Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.7180