Marcinkiewicz integral operators associated with the Dunkl setting and their commutators on some spaces

Key Points

• This research focuses on introducing Marcinkiewicz integral operators related to the Dunkl metric and analyzing their properties.
• Introduced the Marcinkiewicz integral operator Md with specific kernel conditions based on the Dunkl metric.
• Examined the commutators generated by Md with functions in BMO_d on various function spaces.
• Assessed bounding behavior of Md and its commutators on L^p spaces and Morrey spaces related to the Dunkl metric.
• Both the Marcinkiewicz operator Md and the commutator M_{d,b} are confirmed to be bounded on L^p spaces in relation to the Dunkl metric.
• Sharp maximal estimates for Md and M_{d,b} were established, supporting their applicability in the Dunkl setting.