Some new refined general Boas-type inequalities

We state and prove a new refined Boas-type inequality in a setting with a topological space and generalσ-finite and finite Borel measures. As a consequence of the result obtained, we derive a new class of Hardy- and Pólya-Knopp-type inequalities related to balls inℝnand prove that constant factors involved in their right-hand sides are the best possible.