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.
Let , i = 1,2,3, denote positive Borel measures on ℝⁿ, let denote the usual collection of dyadic cubes in ℝⁿ and let K: → [0,∞) be a map. We give a characterization of a trilinear embedding theorem, that is, of the inequality in terms of a discrete Wolff potential and Sawyer’s checking condition, when 1 < p₁,p₂,p₃ < ∞ and 1/p₁ + 1/p₂ + 1/p₃ ≥ 1.
X. Tolsa defined a space of BMO type for positive Radon measures satisfying some growth condition on . This new BMO space is very suitable for the Calderón-Zygmund theory with non-doubling measures. Especially, the John-Nirenberg type inequality can be recovered. In the present paper we introduce a localized and weighted version of this inequality and, as applications, we obtain some vector-valued inequalities and weighted inequalities for Morrey spaces.
A weighted theory describing Morrey boundedness of fractional integral operators and fractional maximal operators is developed. A new class of weights adapted to Morrey spaces is proposed and a passage to the multilinear cases is covered.
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