The Hardy-Littlewood Lemma and the estimate of the $\dib$-Neumann problem in a general norm

TL;DR

This paper extends the Hardy-Littlewood lemma to non-smooth domains using an $f$-norm and applies it to estimate the $ar{ ext{d}}$-Neumann problem with appropriate weights.

Contribution

It introduces a generalized Hardy-Littlewood lemma on non-smooth domains in $f$-norms and applies it to $ar{ ext{d}}$-Neumann problem estimates.

Findings

Established a generalized Hardy-Littlewood lemma for non-smooth domains.

Derived estimates for the $ar{ ext{d}}$-Neumann problem using weighted techniques.

Enhanced understanding of boundary behavior in complex analysis.

Abstract

We prove a generalized Hardy-Littlewood lemma on a non-smooth domain in "$f$-norm" and give an application to a corresponding estimate for the $\dib$-Neumann problem by means of suitable weights.