Weighted $L_{Φ}$ integral inequalities for operators of Hardy type

Tom 110 / 1994

Steven Bloom Studia Mathematica 110 (1994), 35-52 DOI: 10.4064/sm-110-1-35-52

Streszczenie

Necessary and sufficient conditions are given on the weights t, u, v, and w, in order for $Φ_2^{-1} (ʃΦ_2(w(x)|Tf(x)|)t(x)dx) ≤ Φ_{1}^{-1}(ʃΦ_{1}(Cu(x)|f(x)|)v(x)dx)$ to hold when $Φ_1$ and $Φ_2$ are N-functions with $Φ_2∘Φ_{1}^{-1}$ convex, and T is the Hardy operator or a generalized Hardy operator. Weak-type characterizations are given for monotone operators and the connection between weak-type and strong-type inequalities is explored.

Autorzy

  • Steven Bloom

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