A unified approach to fractal Hilbert-type inequalities

Abstract

Abstract In the present study we provide a unified treatment of fractal Hilbert-type inequalities. Our main result is a pair of equivalent fractal Hilbert-type inequalities including a general kernel and weight functions. A particular emphasis is devoted to a class of homogeneous kernels. In addition, we impose appropriate conditions for which the constants appearing on the right-hand sides of the established inequalities are the best possible. As an application, our results are compared with some previously known ones from the literature.

Keywords

• Hilbert inequality
• Conjugate parameters
• Local fractional integral
• Homogeneous function
• The best possible constant