Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Reverse-Holder classes in the Orlicz spaces setting

100%

Harboure E., Salinas O., Viviani B.

Studia Mathematica

1998

tom 130

nr 3

245-261

In connection with the $A_ϕ $ classes of weights (see [K-T] and [B-K]), we study, in the context of Orlicz spaces, the corresponding reverse-Hölder classes $RH_ϕ$. We prove that when ϕ is $Δ_2$ and has lower index greater than one, the class $RH_ϕ$ coincides with some reverse-Hölder class $RH_q,q>1$. For more general ϕ we still get $RH_ϕ ⊂ A_∞ = ⋃_{q>1}RH_q$ although the intersection of all these $RH_ϕ$ gives a proper subset of $⋂_{q>1}RH_q$.

Orlicz boundedness for certain classical operators

100%

Harboure E., Salinas O., Viviani B.

Colloquium Mathematicum

2002

tom 91

nr 2

263-282

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Harboure E.

2 Salinas O.

2 Viviani B.

1 2002

1 1998

Wyniki wyszukiwania

Reverse-Holder classes in the Orlicz spaces setting

Orlicz boundedness for certain classical operators