A New Density Hierarchy Based on Riesz and Hölder Summability

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Abstract
Let f(n) be an Erdős–Ulam function satisfying f(n+1)/f(n)→1 as n→∞, and let Af denote the associated Riesz matrix. Furthermore, let Af* be the Riesz matrix generated by the weights f(n)/f(1)+f(2)+⋯+f(n), n≥1. The main result establishes that the matrix density induced by an arbitrary power of Af—or, equivalently, by a generalized Hölder mean of arbitrary order—is stronger than the matrix density induced by Af*.
Funding Information
  • Ministry of Education, Research, Development and Youth of the Slovak Republic (1/0493/25)

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