A Hilbert-type integral inequality on the fractal space

ABSTRACT

Based on the local fractional calculus, by using the methods of weight function, a Hilbert-type fractal integral inequality and its equivalent form are given. Their constant factors are proved being the best possible, and its applications are discussed briefly.

KEYWORDS:

• Fractal space
• Hilbert-type fractal integral inequality
• weight function

MR(2010)SUBJECT CLASSIFICATION:

• 26D15

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This project was supported by the Scientific Research Fund of Hunan Provincial Education Departments (grant no. 15C1236) and National Natural Science Foundation of China (grant no. 11171280).