Orlicz boundedness for certain classical operators

• Autorzy: E. Harboure , O. Salinas , B. Viviani
• Języki publikacji: EN

Abstrakty

EN

Let ϕ and ψ be functions defined on [0,∞) taking the value zero at zero and with non-negative continuous derivative. Under very mild extra assumptions we find necessary and sufficient conditions for the fractional maximal operator $M_{Ω}^{α}$, associated to an open bounded set Ω, to be bounded from the Orlicz space $L^{ψ}(Ω)$ into $L^{ϕ}(Ω)$, 0 ≤ α < n. For functions ϕ of finite upper type these results can be extended to the Hilbert transform f̃ on the one-dimensional torus and to the fractional integral operator $I_{Ω}^{α}$, 0 <α < n. Since these operators are linear and self-adjoint we get, by duality, boundedness results near infinity, deriving in this way some generalized Trudinger type inequalities.

Kategorie tematyczne

• 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: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 91
• Numer: 2
• Strony: 263-282

Daty

wydano

2002

Twórcy

autor

E. Harboure

• Instituto de Matemática Aplicada del Litoral, Universidad Nacional del Litoral, Güemes 3450, 3000 Santa Fe, Argentina

autor

O. Salinas

• Instituto de Matemática Aplicada del Litoral, Universidad Nacional del Litoral, Güemes 3450, 3000 Santa Fe, Argentina

autor

B. Viviani

• Instituto de Matemática Aplicada del Litoral, Universidad Nacional del Litoral, Güemes 3450, 3000 Santa Fe, Argentina

Identyfikatory

DOI

10.4064/cm91-2-6