Work

Variable Lebesgue Space over Weighted Homogeneous Tree

Year: 2024

Type: article

Abstract: An infinite homogeneous tree is a special type of graph that has a completely symmetrical structure in all directions. For an infinite homogeneous tree T=(V,E) with the natural distance d defined on graphs and a weighted measure μ of exponential growth, the authors introduce the variable Lebesgue space Lp(·)(μ) over (V,d,μ) and investigate it under the global Hölder continuity condition for p(·). As an application, the strong and weak boundedness of the maximal operator relevant to admissible trapezoids on Lp(·)(μ) is obtained, and an unbounded example is presented.

Source: Symmetry

DOI: 10.3390/sym16101283

Authors: Yuxun Zhang, Jiang Zhou

Institution: Xinjiang University

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funder: National Natural Science Foundation of China