# Counterexamples for bi-parameter Carleson embedding

## TL;DR

This paper constructs specific counterexamples demonstrating limitations of the two weight bi-parameter Carleson embedding theorem, highlighting cases where the theorem does not hold.

## Contribution

It provides new counterexamples that challenge the general applicability of the bi-parameter Carleson embedding theorem.

## Key findings

- Counterexamples show the theorem fails in certain cases
- Highlights limitations of existing embedding conditions
- Guides future research on necessary conditions

## Abstract

We build here several counterexamples for two weight bi-parameter Carleson embedding theorem.