Two-weight mixed norm inequalities for maximal operators and extrapolation results for the fractional maximal operator
Sufficient conditions for a two-weight norm inequality for potential type integral operators to hold are given in the case p > q > 0 and p > 1 in terms of the Hedberg-Wolff potential.
We give a characterization of the pairs of weights (v,w), with w in the class of Muckenhoupt, for which the fractional maximal function is a bounded operator from to when 1 < p ≤ q < ∞ and X is a space of homogeneous type.
Necessary and sufficient conditions are shown in order that the inequalities of the form , or hold with some positive C independent of λ > 0 and a μ-measurable function f, where (X,μ) is a space with a complete doubling measure μ, is the maximal operator with respect to μ, Φ, Ψ are arbitrary Young functions, and ϱ, σ are weights, not necessarily doubling.
Let be a nonnegative Borel measure on satisfying that for every cube , where is the side length of the cube and . We study the class of pairs of weights related to the boundedness of radial maximal operators of fractional type associated to a Young function in the context of non-homogeneous spaces related to the measure . Our results include two-weighted norm and weak type inequalities and pointwise estimates. Particularly, we give an improvement of a two-weighted result for certain...