$\theta$-Lebesgue spaces

Traditional Lp spaces are fundamental in functional analysis, demarcated by the relationship $1\mathrm{/}p+1\mathrm{/}q=1$. 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, $1\mathrm{/}(\theta (p))+1\mathrm{/}(\theta (q))=1$. 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.