Estimates for L{\phi}-Lipschitz and L{\phi}-BMO Norms of Differential Forms

TL;DR

This paper introduces new norms for differential forms based on Young functions, establishes comparison theorems for the homotopy operator, and provides estimates for conjugate A-harmonic tensors and weighted Lipschitz norms.

Contribution

It defines Lφ-Lipschitz and Lφ-BMO norms for differential forms and proves comparison theorems, advancing the analysis of these forms in geometric analysis.

Findings

Comparison theorems for homotopy operator T with Lφ norms

Lφ-BMO norm estimates for conjugate A-harmonic tensors

Weighted Lφ-Lipschitz norm estimates for the homotopy operator T

Abstract

In this paper, we define the L{\phi}-Lipschitz norm and L{\phi}-BMO norm of differential forms using Young functions, and prove the comparison theorems for the homotopy operator T on differential forms with L{\phi}-Lipschitz and L{\phi}-BMO norms. As applications, we give the L{\phi}-BMO norm estimate for conjugate A-harmonic tensors and the weighted L{\phi}-Lipschitz norm estimate for the homotopy operator T.