Sharp Hardy inequalities of fractional order involving slowly varying functions

Abstrakt

We establish necessary and sufficient conditions for the validity of Hardy inequalities of fractional orders involving weights which are products of power-type functions and slowly varying functions. Consequently, for such weights, we solve Open Problems 1 and 2 mentioned in the book of Kufner and Persson, Weighted Inequalities of Hardy Type (World Scientific Publishing, 2003).

Klíčová slova

• Hardy inequality of fractional order
• Slowly varying functions