Hypercontractivity Inequality on $\varepsilon$-product Spaces
summary
Proves a (2,4)-hypercontractivity inequality for general ε-product spaces including spectral high‑dimensional expanders, with a bound that applies to degree‑d, d‑delta global functions and an error term growing with ε and k and a crude coefficient like 400·d^d. Proof uses orthogonal Efron–Stein projections and Efron–Stein decomposition plus derivative operators and induction on degree, adapts coupling/log‑Sobolev ideas to handle near‑product correlations, and recovers earlier product‑space cases though with weaker parameters than specialized HDX results.
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