Stein’s dimension-free weak-(1,1) Riesz transform problem

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Corrects Stein’s dimension-free weak-(1,1) Riesz transform problem →

Supersedes Stein’s dimension-free weak-(1,1) Riesz transform problem →

Stein’s dimension-free weak-(1,1) Riesz transform problem parent of this event

This event attributed to Cody B. Stockdale

This event attributed to Yuyuan Ouyang

This event attributed to Daniel Spector

The theorem is the vector-valued endpoint bound $\|Rf\|_{L^{1,\infty}} \le 2\|f\|_{L^1}$ for $R = (R_1,\ldots,R_n)$, so the constant 2 also serves each component $R_j$ uniformly in the dimension; the best previously known component bound grew like $c\log n$. The mechanism is a decomposition theorem stated as Theorem 1.2: for every nonnegative $f \in L^1 \cap L^2$ and every $\lambda > 0$, write $f = \mu + (-\Delta)^{\alpha/2}u$ with $\mu \le \lambda$ and $u$ in the fractional Sobolev space $H^\alpha$, obtained from an obstacle problem for the fractional Laplacian together with a Lewy-Stampacchia type estimate on an unbounded domain. That replaces the Calderon-Zygmund decomposition, whose cube geometry is where the dimensional loss enters. parent of this event

This event attributed to Claude Opus 5.0

Stein’s dimension-free weak-(1,1) Riesz transform problem evidence for this event

VibeMathed record: Stein’s dimension-free weak-(1,1) Riesz transform problem evidence for this event

This event attributed to GPT-5.6 Sol

Spector and Stockdale (2020), the reduction to Dirac masses this paper grew out of evidence for this event