arXiv subjects

Ryutaro Arai

Publications and source records attributed to Ryutaro Arai.

2 recordsLinked to original sources

arXiv2020

Commutators of integral operators with functions in Campanato spaces on Orlicz-Morrey spaces

We consider the commutators $[b,T]$ and $[b,I_ρ]$ on Orlicz-Morrey spaces, where $T$ is a Calderón-Zygmund operator, $I_ρ$ is a generalized fractional integral operator and $b$ is a function in generalized Campanato spaces. We give a necessary and sufficient condition for the boundedness of the commutators on Orlicz-Morrey spaces. To do this we prove the boundedness of generalized fractional maximal operators on Orlicz-Morrey spaces. Moreover, we introduce Orlicz-Campanato spaces and establish their relations to Orlicz-Morrey spaces.

math.FA↗

arXiv2018

Generalized fractional integral operators and their commutators with functions in generalized Campanato spaces on Orlicz spaces

We investigate the commutators $[b,I_ρ]$ of generalized fractional integral operators $I_ρ$ with functions $b$ in generalized Campanato spaces and give a necessary and sufficient condition for the boundedness of the commutators on Orlicz spaces. To do this we define Orlicz spaces with generalized Young functions and prove the boundedness of generalized fractional maximal operators on the Orlicz spaces.

math.FA↗