# On a weak type estimate for sparse operators of strong type

## TL;DR

This paper establishes weak and strong type inequalities for sparse operators of strong type within abstract measure spaces, advancing the theoretical understanding of these operators in harmonic analysis.

## Contribution

It introduces a framework for sparse operators of strong type on abstract measure spaces and proves related weak and strong type inequalities.

## Key findings

- Proved weak type inequalities for sparse operators.
- Established strong type inequalities for these operators.
- Extended the theory to abstract measure spaces with ball-bases.

## Abstract

We define sparse operators of strong type on abstract measure spaces with ball-bases. Weak and strong type inequalities for such operators are proved.