Pitt inequality for the linear structurally damped $\sigma$-evolution equations

TL;DR

This paper improves decay estimates for solutions to linear structurally damped $\sigma$-evolution equations using Pitt inequalities, focusing on initial data in weighted spaces.

Contribution

It introduces enhanced decay estimates for these equations by applying Pitt inequalities to initial data in weighted spaces, advancing previous decay analysis.

Findings

Improved decay rates for solutions and derivatives.

Effective use of Pitt inequality in the analysis.

Applicable to initial data in weighted spaces.

Abstract

This work is devoted to improve the time decay estimates for the solution and some of its derivatives of the linear structurally damped $\sigma$-evolution equations. The Pitt inequality is the main tool provided that the initial data lies in some weighted spaces.