Boundedness of the Riesz potential in central Morrey--Orlicz spaces
Evgeniya Burtseva, Lech Maligranda, Katsuo Matsuoka
TL;DR
This paper establishes the boundedness of the Riesz potential operator in central Morrey-Orlicz spaces, extending previous results on maximal functions and singular integrals, and includes weak-type estimates.
Contribution
It introduces the boundedness of the Riesz potential in central Morrey-Orlicz spaces, a novel extension of prior work on related operators.
Findings
Boundedness of the Riesz potential in central Morrey-Orlicz spaces
Weak-type estimates for the Riesz potential
Extension of boundedness results to new operator class
Abstract
Boundedness of the maximal function and the Calde\'on-Zygmund singular integrals in central Morrey-Orlicz spaces were proved in papers by the second and third authors. The weak-type estimates have also been proven. Here we show boundedness of the Riesz potential in central Morrey-Orlicz spaces and the corresponding weak-type version.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Advanced Mathematical Physics Problems · Nonlinear Partial Differential Equations