Generalized fractional integral operators and fractional maximal operators in the framework of Morrey spaces

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A Thought on Generalized Morrey Spaces (2018, methodology): “ID 835865, 18 pp. [104] Y. Sawano, S. Sugano and H. Tanaka, Generalized fractional integral operators and fractional maximal operators in the framework of Morrey spaces, Trans.”
Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces (2013, unknown): “By Sobolev embedding (1.2) we also deduce ũn → w in L2 ∗ , hence ∫ |w|2∗dx = S∗ and w is an optimal function in the Sobolev inequality (1.5), thus w is given by (1.4) in view of [11, Theorem 1.1].”
Orlicz–Morrey Spaces and Fractional Operators (2012, methodology): “In our previous papers [16] and [17] we have assumed that ρ satisfies 1 C ≤ ρ(s) ρ(t) ≤ C, if 1 2 ≤ s t ≤ 2.”
Generalized weighted Morrey spaces and classical operators (2016, unknown): “The maximal operator M was generalized in [29] as follows: For a function ρ : [0,∞) → [0,∞), define the generalized fractional maximal operator Mρ by Mρ f (x) := sup Q∈D ρ( (Q)) |Q| ∫”
FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, unknown): “The generalized fractional integral operators Iρ with ρ : (0,∞) → (0,∞) are studied in [144, 145, 146, 149, 206, 207] and the spaces L(R) with constant p and φ : R × (0,∞) → (0,∞) are studied in [142, 147, 151, 157].”