A note on $L^p_{w}(\nu,X,Y)$ spaces of vector-valued functions with respect to vector measures

TL;DR

This paper introduces and studies the properties of new vector-valued function spaces, denoted as $L^p_{w}( u; X; Y)$, where $ u$ is a vector measure, expanding the theoretical framework for analysis involving vector measures.

Contribution

The paper defines the spaces $L^p_{w}( u; X; Y)$ for vector measures and establishes their fundamental properties, contributing to the theory of vector-valued function spaces.

Findings

Defined the spaces $L^p_{w}( u; X; Y)$ for vector measures.

Proved fundamental properties of these spaces.

Extended the theory of vector-valued function spaces.

Abstract

In this work we introduce the spaces $L^p_{w}(\nu; X; Y)$ for the case where $\nu$ is a vector measure and the functions are vector-valued. We establish fundamental properties for such spaces.