On generalized fractional integrals on the weak Orlicz spaces, BMO_φ, the Morrey spaces and the Campanato spaces

By E. Nakai. 2002

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Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials (2010, background): “The first part ‖Iρf‖L(1,ψ)(G) ≤ C‖f‖L(1,φ)(G) is proved in [16] when G = R and dG = ∞.”
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.”
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].”