Embedding theorems for harmonic multifunctional spaces on R^n+1

TL;DR

This paper introduces new multifunctional harmonic spaces in the upper halfspace and establishes sharp embedding theorems, advancing understanding even for single-function cases.

Contribution

It presents novel properties and sharp embedding theorems for multifunctional harmonic spaces, extending existing theory to new multi-function contexts.

Findings

Established sharp embedding theorems for multifunctional harmonic spaces

Demonstrated new properties of these spaces in the upper halfspace

Results are novel even for single-function harmonic spaces

Abstract

We introduce and study properties of certain new multifunctional harmonic spaces in the upper halfspace.We prove several sharp embedding theorems for such multifunctional spaces,these results are new even in the case of a single function.