Weighted norm inequalities for pseudo-differential operators and their commutators

TL;DR

This paper establishes new weighted inequalities for pseudo-differential operators and their commutators using expanded weight and BMO classes, leading to significant improvements over classical results.

Contribution

It introduces larger classes of weights and BMO functions, extending the scope of weighted inequalities for pseudo-differential operators and their commutators.

Findings

Improved weighted $L^p$ inequalities for pseudo-differential operators.

Extended classes of weights $A_p^ u$ and BMO$_ u$.

Enhanced bounds compared to classical results.

Abstract

This paper is dedicated to study weighted $L^p$ inequalities for pseudo-differential operators with amplitudes and their commutators by using the new class of weights $A_p^\vc$ and the new BMO function space BMO$_\vc$ which are larger than the Muckenhoupt class of weights $A_p$ and classical BMO space BMO, respectively. The obtained results therefore improve substantially some well-known results.