Weighted composition operators on bicomplex Lorentz spaces with their characterization and properties

Abstract

This article presents a characterization of non-singular measurable transformation, denoted as TT, mapping from Ω\Omega to itself, along with bicomplex-valued BC{\mathbb{BC}}-measurable function uu defined on Ω\Omega , which induces a weighted composition operator. The study then proceeds to fully identify their D{\mathbb{D}}-compactness and D{\mathbb{D}}-closedness within the range of bicomplex Lorentz spaces denoted as Lp,qBC(Ω,M,ϑ){L}_{p,q}^{{\mathbb{BC}}}(\Omega ,{\mathfrak{M}},{\vartheta }), where (Ω,M,ϑ)(\Omega ,{\mathfrak{M}},{\vartheta }) represents a σ\sigma -finite complete BC{\mathbb{BC}}-measure space, ϑ=ϑ1e1+ϑ2e2{\vartheta }={{\vartheta }}_{1}{e}_{1}+{{\vartheta }}_{2}{e}_{2} is a BC{\mathbb{BC}}-measure, and the parameters satisfy 1<p≤∞1\lt p\le \infty , 1≤q≤∞1\le q\le \infty .

Keywords

• bicomplex numbers
• bc-valued functions
• hyperbolic norm
• 𝔻-distribution function
• 𝔻-rearrangement
• multiplication operator
• composition operator
• 47b38
• 30g35
• 46e30