On Unconditional Basis of Weightd Lp Space

Abdulkrem Mhamdhsan Abdlwhab

Abdulkrem Mhamdhsan Abdlwhab Directorate of Education of Dhi Qar, Iraq

Keywords: Unconditional Basis, Mathematics, Analysis

Abstract

This study delves into the exploration of unconditional bases within weighted LpLp spaces, which are extensions of classical LpLp spaces incorporating weight functions into integrability conditions. Such spaces are pivotal in diverse mathematical and engineering applications like differential equations and signal processing. However, the existence and properties of unconditional bases in these spaces remain underexplored. We investigate conditions under which various classes of weight functions enable the existence of unconditional bases and analyze their structural characteristics. Employing a blend of analytical techniques from functional analysis and numerical simulations, we identify polynomial and wavelet bases that offer unconditional convergence in specific weighted LpLp settings, contingent upon properties of the weight function. We also elucidate how variations in weight functions influence the unconditional nature and utility of these bases, providing deeper insights into their behavior in both theoretical and practical contexts. This research not only advances understanding of weighted LpLp spaces but also underscores their significant implications for solving complex real-world problems.

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