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Weighted inequalities for one-sided maximal functions in Orlicz spaces

100%

Ortega Salvador P.

Studia Mathematica

1998

tom 131

nr 2

101-114

Let $M_{g}^{+}$ be the maximal operator defined by $M_{g}^{+}⨍(x) = sup_{h>0} (ʃ_{x}^{x+h} |⨍|g)/(ʃ_{x}^{x+h} g)$, where g is a positive locally integrable function on ℝ. Let Φ be an N-function such that both Φ and its complementary N-function satisfy $Δ_2$. We characterize the pairs of positive functions (u,ω) such that the weak type inequality $u({x ∈ ℝ | M_{g}^{+}⨍(x) > λ}) ≤ C/(Φ(λ)) ʃ_ℝ Φ(|⨍|)ω$ holds for every ⨍ in the Orlicz space $L_Φ(ω)$. We also characterize the positive functions ω such that the integral inequality $ʃ_ℝ Φ(|M_{g}^{+}⨍|)ω ≤ ʃ_ℝ Φ(|⨍|)ω$ holds for every $⨍ ∈ L_Φ(ω)$. Our results include some already obtained for functions in $L^p$ and yield as consequences one-dimensional theorems due to Gallardo and Kerman-Torchinsky.

Weighted estimates for commutators of linear operators

100%

Alvarez J., Bagby R. J., Kurtz D. S., Pérez C.

Studia Mathematica

1993

tom 104

nr 2

195-209

We study boundedness properties of commutators of general linear operators with real-valued BMO functions on weighted $L^p$ spaces. We then derive applications to particular important operators, such as Calderón-Zygmund type operators, pseudo-differential operators, multipliers, rough singular integrals and maximal type operators.

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Essential norm estimates for multilinear singular and fractional integrals

88%

Meskhi A.

Commentationes Mathematicae

2019

tom 59

nr 1-2

We derive lower two-weight estimates for the essential norm (measure of noncompactness) for multilinear Hilbert and Riesz transforms, and Riesz potential operators in Banach function lattices. As a corollary we have appropriate results in weighted Lebesgue spaces. From these statements we conclude that there is no $(m+1)$-tuple of weights $(v,w_1, \dots, w_m)$ for which these operators are compact from $L^{p_1}_{w_1} \times \dots \times L^{p_m}_{w_m}$ to $L^q_v$.

Ograniczanie wyników

2 Studia Mathematica

1 Commentationes Mathematicae

1 Alvarez J.

1 Bagby R. J.

1 Kurtz D. S.

1 Meskhi A.

1 Ortega Salvador P.

1 Pérez C.

1 2019

1 1998

1 1993

Wyniki wyszukiwania

Weighted inequalities for one-sided maximal functions in Orlicz spaces

Weighted estimates for commutators of linear operators

Essential norm estimates for multilinear singular and fractional integrals