# T(1) theorem for dyadic singular integral forms associated with hypergraphs

## TL;DR

This paper establishes T(1) theorems for dyadic singular integrals linked to hypergraphs, providing boundedness criteria, sparse domination, and weighted estimates with multilinear Muckenhoupt weights.

## Contribution

It introduces new T(1) criteria for hypergraph-associated dyadic singular integrals and extends weighted bounds using sparse domination techniques.

## Key findings

- Characterization of $L^p$ boundedness via T(1)-type conditions.
- Sparse domination of the singular integral forms.
- Weighted estimates with multilinear Muckenhoupt weights.

## Abstract

This paper studies dyadic singular integral forms associated with $r$-partite $r$-uniform hypergraphs such that all their connected components are complete. We characterize their $L^p$ boundedness by T(1)-type conditions in two different ways. We also dominate these forms by positive sparse forms and prove weighted estimates with multilinear Muckenhoupt weights.