Embeddings of Lorentz-type spaces involving weighted integral means

Abstract

We solve the problem of characterizing weights on (0, infinity) for which the inequality involving two possibly different general inner weighted means (integral(infinity)(0)(integral(t)(0)f*(s)(m2)u(2)(s)ds)(p2/m2) w(2)(t)dt)(1/p2) m(2). The proof is based on a new approach combining duality techniques with sharp weighted estimates for iterated integral and supremum operators.

Keywords

• Weighted inequalities
• Iterated operators
• Classical Lorentz spaces
• Embeddings