Sufficient and necessary conditions for generalized H\"older's inequality in p-summable sequence spaces

TL;DR

This paper establishes the precise conditions under which the generalized H"older's inequality holds in p-summable sequence spaces, enhancing the theoretical understanding of inequalities in functional analysis.

Contribution

It provides the first complete characterization of necessary and sufficient conditions for the generalized H"older's inequality in p-summable sequence spaces.

Findings

Derived necessary and sufficient conditions for the inequality.

Estimated norms of characteristic sequences in \\mathbb{R}.

Enhanced theoretical framework for inequalities in sequence spaces.

Abstract

In this paper, we discuss the generalized H\"older's inequality in p-summable sequence spaces. In particular, we shall prove sufficient and necessary conditions for generalized H\"older's inequality in those spaces. One of the keys to prove our results is to estimate the norms of characteristic sequences in \mathbb{R}.