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- On the Riesz potential operator of variable order from variable exponent Morrey space to variable exponent Campanato spacePublication . Rafeiro, Humberto; Samko, StefanFor the Riesz potential of variable order over bounded domains in Euclidean space, we prove the boundedness result from variable exponent Morrey spaces to variable exponent Campanato spaces. A special attention is paid to weaken assumptions on variability of the Riesz potential.
- A note on vanishing Morrey -> VMO result for fractional integrals of variable orderPublication . Rafeiro, Humberto; Samko, StefanIn the limiting case of Sobolev-Adams theorem for Morrey spaces of variable order we prove that the fractional operator of variable order maps the corresponding vanishing Morrey space into VMO.
- Addendum to “On the Riesz potential operator of variable order from variable exponent Morrey space to variable exponent Campanato space”, Math Meth Appl Sci. 2020; 1–8Publication . Rafeiro, Humberto; Samko, StefanIn the paper mentioned in the title, it is proved the boundedness of the Riesz potential operator of variable order 𝛼(x) from variable exponent Morrey space to variable exponent Campanato space, under certain assumptions on the variable exponents p(x) and 𝜆(x) of the Morrey space. Assumptions on the exponents were different depending on whether 𝛼(x)p(x)−n+𝜆(x) p(x) takes or not the critical values 0 or 1. In this note, we improve those results by unifying all the cases and covering the whole range 0 ⩽ 𝛼(x)p(x)−n+𝜆(x) p(x) ⩽ 1. We also provide a correction to some minor technicality in the proof of Theorem 2 in the aforementioned paper.