The Douglas formula in $L^p$

TL;DR

This paper establishes a Douglas-type identity within the framework of L^p spaces for the range 1<p<∞, extending classical results to a broader functional setting.

Contribution

It introduces a new Douglas formula applicable to L^p spaces, broadening the scope of classical identities beyond Hilbert spaces.

Findings

Proves a Douglas-type identity in L^p spaces for 1<p<∞

Extends classical Hilbert space results to Banach spaces

Provides foundational tools for analysis in L^p contexts

Abstract

We prove a Douglas-type identity in $L^p$ for $1<p<\infty$.