Estimates for norms of two-weighted summation operators on trees for $1<p<q<\infty$

TL;DR

This paper derives estimates for the norms of weighted summation operators, akin to discrete Hardy operators, on trees for a range of p and q values, considering arbitrary weights and tree structures.

Contribution

It provides new norm estimates for weighted summation operators on trees applicable to all weights and tree configurations within the specified p and q range.

Findings

Derived explicit norm estimates for weighted summation operators on trees

Applicable to arbitrary weights and tree structures

Extends previous results to a broader class of operators and settings

Abstract

In this paper, estimates for norms of weighted summation operators (discrete Hardy-type operators) on a tree are obtained for $1<p<q<\infty$ and for arbitrary weights and trees.