A note on the boundedness of discrete commutators on Morrey spaces and their preduals

TL;DR

This paper proves the boundedness of dyadic fractional integral operators and their commutators on Morrey spaces and their preduals, highlighting the effectiveness of dyadic methods especially on preduals.

Contribution

It establishes the boundedness of discrete commutators on Morrey spaces and their preduals, extending previous results on fractional integral operators.

Findings

Dyadic fractional integral operators are bounded on Morrey spaces.

Commutators of these operators are also bounded on the same spaces.

Dyadic methods are particularly effective on preduals.

Abstract

Dyadic fractional integral operators are shown to be bounded on Morrey spaces and their preduals. It seems that the proof of the boundedness by means of dyadic fractional integral operators is effective particularly on the preduals. In the present paper the commutators are proved to be bounded as well.