Average operators on rectangular Herz spaces

TL;DR

This paper introduces rectangular Herz spaces and investigates the continuity properties of average operators acting on these new function spaces.

Contribution

It presents a novel family of Herz spaces based on rectangles and analyzes the behavior of average operators within these spaces.

Findings

Rectangular Herz spaces are well-defined and exhibit specific continuity properties.

Average operators are shown to be continuous on these spaces under certain conditions.

The work extends classical Herz space theory to a new geometric setting.

Abstract

We introduce a family or Herz type spaces considering rectangles instead of balls and we study continuity properties of some average operators acting on them