Weighted Fourier Inequalities: New Proofs and Generalizations

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Limiting reiteration for real interpolation with slowly varying functions (2005, result): “3) Here θ ∈ [0, 1], q ∈ (0,∞], ‖ · ‖q,(c,d) , −∞ ≤ c < d ≤ ∞, is the standard L-quasinorm on (c, d) with respect to the Lebesgue measure, and (t) denotes the broken logarithmic function given by”
Net Spaces and Boundedness of Integral Operators (2011, background): “The boundedness of the Hardy-type transforms, the potential operators, the Laplace and Fourier transforms, and the Riemann–Liouville operators in the weighted spaces have been extensively studied, and in many cases the complete answers were presented as criteria in terms of weights (see the books [1”