# From dyadic $\Lambda_{\alpha}$ to $\Lambda_{\alpha}$

## TL;DR

This paper demonstrates how to compute the $\Lambda_{\alpha}$ norm using dyadic grids, linking it to the characterization of Hardy spaces via dyadic and special atoms.

## Contribution

It provides a method to compute the $\Lambda_{\alpha}$ norm through dyadic grids based on Hardy space atom descriptions.

## Key findings

- $\Lambda_{\alpha}$ norm can be computed using dyadic grids
- Connection established between $\Lambda_{\alpha}$ norms and Hardy space atoms
- Simplifies analysis of function spaces using dyadic structures

## Abstract

In this paper we show how to compute the $\Lambda_{\alpha}$ norm, $\alpha\ge 0$, using the dyadic grid. This result is a consequence of the description of the Hardy spaces $H^p(R^N)$ in terms of dyadic and special atoms.