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

• Autorzy: Steven Bloom , Ron Kerman
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 26D15: Inequalities for sums, series and integrals
• 26A33: Fractional derivatives and integrals
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 110
• Numer: 1
• Strony: 35-52

Daty

wydano

1994

otrzymano

1993-03-18

Twórcy

autor

Steven Bloom

• Department of Mathematics, Siena College, Loudonville, New York 12211, U.S.A.

autor

Ron Kerman

• Department of Mathematics, Brock University, St. Catharines, Ontario, Canada LS2A1

Bibliografia

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