# On the Generalized Quotient Integrals on Homogenous Spaces

## TL;DR

This paper generalizes the quotient integral formula for homogeneous spaces, explores its properties, and examines relationships between function spaces, supported by examples.

## Contribution

It introduces a generalized quotient integral formula and investigates its properties and applications to function spaces on homogeneous spaces.

## Key findings

- Derived relations between function spaces on homogeneous spaces.
- Established properties of the generalized quotient integral formula.
- Provided examples illustrating the theoretical results.

## Abstract

A generalization of the quotient integral formula is presented and some of its properties are investigated. Also the relations between two function spaces related to the spacial homogeneous spaces are derived by using general quotient integral formula. Finally our results are supported by some examples.