Year: 2019
Type: preprint
Abstract: We prove that the discrete fractional integration operators along the primes \[ T^λ_{\mathbb{P}}f(x) := \sum_{p} \frac{f(x-p)}{p^λ} \cdot \log p \] are bounded $\ell^p\to \ell^{p'}$ whenever $ \frac{1}{p'} < \frac{1}{p} - (1-λ), \ p > 1.$ Here, the sum runs only over prime $p$.
Source: arXiv (Cornell University)
Author: Krause, Ben
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2943961970