Necessary and Sufficient Conditions for the Boundedness of the Riesz Potential in Local Morrey-type Spaces

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Boundedness of the maximal, potential and singular operators in the generalized variable exponent Morrey spaces (2010, background): “In the case of constant p and λ, the results on the boundedness of potential operators and classical CalderonZygmund singular operators go back to [1] and [32], respectively, while the boundedness of the maximal operator in the Euclidean setting was proved in [9]; for further results in the case of ”
Calderón–Zygmund operators in Morrey spaces (2014, background): “One may consult the recent papers [4,16,21] and the references within.”
Generalized Local Morrey Spaces and Fractional Integral Operators with Rough Kernel (2012, background): “In [6] also other examples of operators which are estimates from above by Riesz potentials are given.”
Characterizations For The Generalized Fractional Integral Operators On Morrey Spaces (2014, methodology): “In order to highlight what we shall prove in this paper, we take up the works [3, 6, 7, 18, 22, 25, 28, 35], where we formulated sufficient conditions on ρ for Iρ to be bounded on Morrey spaces Lp,φ with 1 6 p < ∞ and φ a function from (0,∞) to itself.”
Maximal functions, potentials and singular integrals in grand Morrey spaces (2011, background): “Finally we mention that necessary and sufficient conditions for the boundedness of maximal operators and Riesz potentials in the local Morrey-type spaces were derived in 17 , 18 .”