Differentiating Orlicz spaces with rare bases of rectangles

TL;DR

This paper investigates how the rate at which angles decrease affects the construction of specialized rectangle bases that differentiate a specific Orlicz space, revealing the relationship between geometric configurations and functional space properties.

Contribution

It introduces a novel analysis linking the convergence speed of angle sequences to the ability to construct rare differentiation bases for Orlicz spaces.

Findings

Speed of angle convergence influences basis construction

Constructs bases that differentiate a fixed Orlicz space

Establishes conditions for basis differentiation capabilities

Abstract

In the current paper, we study how the speed of convergence of a sequence of angles decreasing to zero influences the possibility of constructing a rare differentiation basis of rectangles in the plane, one side of which makes with the horizontal axis an angle belonging to the given sequence, that differentiates precisely a fixed Orlicz space.