About the Hardy Inequality

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Weighted Hardy operators in the local generalized vanishing Morrey spaces (2012, unknown): “The L p → Lq -boundedness of the multidimensional Hardy operators within the frameworks of Lebesgue spaces (the case φ ≡ 1) with 1 < p < ∞ and 0 < q < ∞ is known, see for instance, [9,12,13,20].”
Global Existence of Smooth Solutions and Convergence to Barenblatt Solutions for the Physical Vacuum Free Boundary Problem of Compressible Euler Equations with Damping (2014, background): “[16]): H(I) →֒ H(I) with the estimate ‖F‖Hb−a/2(I) ≤ C(a, b)‖F‖Ha,b(I) (3.”
Factorizations and Hardy’s type identities and inequalities on upper half spaces (2019, background): “Hence, we just refer the interested reader to [32,49] for historical backgrounds and to the monographs [3,33,34,55], that are standard references on the topic.”