Year: 2024
Type: preprint
Abstract: Traditional Lp spaces are fundamental in functional analysis, demarcated by the relationship $1/p + 1/q = 1$. This research pioneers the concept of $θ$-Lebesgue space, stemming from a simultaneous weakening of both the classical $L_p$ relation and its $θ$-variant, $1/(θ(p)) + 1/(θ(q)) = 1$. 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 $θ$-Lebesgue space within this new context, explore its foundational properties, and articulate its theoretical significance in the realm of functional analysis.
Source: arXiv (Cornell University)
Author: Choudhury, Shouvik Datta
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4390962098