Weighted norm inequalities for pseudo-differential operators with smooth symbols and their commutators

TL;DR

This paper establishes new weighted inequalities for pseudo-differential operators with smooth symbols and their commutators, expanding the class of applicable weight functions and improving existing results in the field.

Contribution

It introduces a new class of weight functions, including Muckenhoupt weights, to derive improved weighted $L^p$ inequalities for these operators and their commutators.

Findings

Weighted $L^p$ inequalities are established for pseudo-differential operators.

The results include a broader class of weight functions, such as Muckenhoupt weights.

The inequalities improve upon previously known results in the literature.

Abstract

We obtain weighted $L^p$ inequalities for pseudo-differential operators with smooth symbols and their commutators by using a class of new weight functions which include Muckenhoupt weight functions. Our results improve essentially some well-known results.