The relationship between some special conditions of young functions and the validity of generalized $L^p$ estimate for the Poisson equations in a unit ball

TL;DR

This paper investigates how specific conditions of Young functions influence the validity of generalized L^p estimates for Poisson equations in a unit ball, linking functional conditions to PDE estimates.

Contribution

It establishes a connection between Young function conditions and the validity of generalized L^p estimates for Poisson equations in a bounded domain.

Findings

Global Δ₂ and ∇₂ conditions of Young functions are crucial for generalized L^p estimates.

The paper characterizes when these estimates hold based on Young function properties.

Results apply to Poisson equations in the unit ball domain.

Abstract

In this paper, we consider the domain is in $B_1$, and we will show the relationship between the global $\Delta_2$ and $\nabla_2$ conditions of young functions and the validity of generalized $L^p$ estimate for the Poisson equations.