# A note on generalized Fujii-Wilson conditions and BMO spaces

## TL;DR

This paper generalizes Fujii-Wilson conditions to characterize classes of weights like A_infinity and C_p using BMO-type spaces, offering new self-improvement properties and quantitative estimates.

## Contribution

It introduces a generalized framework for Fujii-Wilson conditions and connects them to BMO spaces for various weight classes, with new self-improvement results.

## Key findings

- Quantitative characterizations of A_infinity, A_infinity^{weak}, and C_p.
- Self-improvement properties for generalized BMO spaces.
- Quantitative estimates for Bloom's BMO spaces.

## Abstract

In this note we generalize the definition of Fujii-Wilson condition providing quantitative characterizations of some interesting classes of weights, such as $A_\infty$, $A_\infty^{weak}$ and $C_p$, in terms of BMO type spaces suited to them. We will provide as well some self improvement properties for some of those generalized BMO spaces and some quantitative estimates for Bloom's BMO type spaces.