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Two-weight norm inequalities for the fractional maximal operator on spaces of homogeneous type

Ana Bernardis; Oscar Salinas — 1994

Studia Mathematica

We give a characterization of the pairs of weights (v,w), with w in the class $A_{\infty}$ of Muckenhoupt, for which the fractional maximal function is a bounded operator from $L^{p} (X, v d μ)$ to $L^{q} (X, w d μ)$ when 1 < p ≤ q < ∞ and X is a space of homogeneous type.

Two weighted inequalities for convolution maximal operators.

Ana Lucía Bernardis; Francisco Javier Martín-Reyes — 2002

Publicacions Matemàtiques

Let φ: R → [0,∞) an integrable function such that φχ = 0 and φ is decreasing in (0,∞). Let τf(x) = f(x-h), with h ∈ R {0} and f(x) = 1/R f(x/R), with R > 0. In this paper we characterize the pair of weights (u, v) such that the operators Mf(x) = sup|f| * [τφ](x) are of weak type (p, p) with respect to (u, v), 1 < p < ∞.

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