Embeddings of Lorentz-type spaces involving weighted integral means

作者：Gogatishvili Amiran; Krepela Martin; Pick Lubos^*; Soudsky Filip

来源：Journal of Functional Analysis, 2017, 273(9): 2939-2980.

DOI：10.1016/j.jfa.2017.06.008

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

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)
<= C(integral(infinity)(0)(integral(t)(0)f*(s)(m2)u(1)(s)ds)(p1/m1) w(1)(t)dt)(1/p1)
holds, where p(1), p(2), m(1), m(2) is an element of (0, infinity) and p(2) > m(2). The proof is based on a new approach combining duality techniques with sharp weighted estimates for iterated integral and supremum operators.

• 出版日期2017-11-1