Some new moment rearrangement invariant spaces; theory and applications

TL;DR

This paper introduces new moment rearrangement invariant Banach spaces and explores their applications in Fourier analysis, singular integrals, and martingale theory, expanding the functional analysis toolkit.

Contribution

It presents novel moment spaces and demonstrates their utility in various areas of analysis, a new development in Banach space theory.

Findings

Defined new Banach spaces called moment spaces

Applied these spaces to Fourier series and singular integrals

Extended the theory to martingales

Abstract

In this article we introduce and investigate some new Banach spaces, so - called moment spaces, and consider applications to the Fourier series, singular integral operators, theory of martingales.