$\theta$-Lebesgue spaces

Abstract

Traditional Lp spaces are fundamental in functional analysis, demarcated by the relationship $1/p + 1/q = 1$. This research pioneers the concept of $\theta$-Lebesgue space, stemming from a simultaneous weakening of both the classical $L_p$ relation and its $\theta$-variant, $1/(\theta(p)) + 1/(\theta(q)) = 1$. This conceptual shift addresses a gap in existing mathematical frameworks, aiming to create a space that encompasses a broader range of mathematical purpose. The primary objective is to rigorously demarcate the $\theta$-Lebesgue space within this new context, explore its foundational properties, and articulate its theoretical significance in the realm of functional analysis.