2 problems

Multilinear Marcinkiewicz integral extrapolation conjecture. If $\mu$ is bounded from $L^{q_1}({\mathbb R}^n)\times\cdots\times L^{q_m}({\mathbb R}^n)$ to $L^q({\mathbb R}^n)$ for…

In 1938, Marcinkiewicz introduced the integral on the one-dimensional Euclidean space $\mathbb R$, now called the Marcinkiewicz integral. For $p\in(1,\infty)$, consider the space…