Abstract Consider averages along the prime integers ℙ given by {\mathcal{A}_N}f(x) = {N^{ - 1}}\sum\limits_{p \in \mathbb{P}:p \le N} {(\log p)f(x - p).} These averages satisfy a uniform scale-free ℓ p -improving estimate. For all 1 < p < 2, there is a constant C p so that for all integer N and functions f supported on [0, N ], there holds {N^{ - 1/p'}}{\left\| {{\mathcal{A}_N}f} \right\|_{\ell p'}} \le {C_p}{N^{ - 1/p}}{\left\| f \right\|_{\ell p}}. The maximal function 𝒜 * f = sup N |𝒜 N f | satisfies ( p , p ) sparse bounds for all 1 < p < 2. The latter are the natural variants of the scale-free bounds. As a corollary, 𝒜 * is bounded on ℓ p ( w ), for all weights w in the Muckenhoupt 𝒜 p class. No prior weighted inequalities for 𝒜 * were known.
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Atomistic simulations of mechanically activated reactions for oxygen release from polymers
Reactive molecular dynamics simulations differentiate thermal and mechanochemical pathways for oxygen release from polymers with implications for therapeutic applications.
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- Award ID(s):
- 2303044
- PAR ID:
- 10608486
- Publisher / Repository:
- Royal Society of Chemistry
- Date Published:
- Journal Name:
- RSC Mechanochemistry
- Volume:
- 1
- Issue:
- 4
- ISSN:
- 2976-8683
- Page Range / eLocation ID:
- 361 to 366
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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