Research proof index

The first column of the Lorentz matrix formed from an element of SL(2, ℂ).

Two Lorentz transformations which are in the same connected component are either both orthochronous or both not orthochronous.

A matrix Λ is in the Lorentz group if and only if it satisfies Λᵀ * η * Λ = η.

At every point $x$, the magnitude of the Carleson sum over an antichain of tiles is bounded by a constant depending on $a$ times a maximal function of $f$. The maximal function uses, for each tile $p$, a ball centered at the tile center with radius $8D^{\mathfrak{s}(p)}$.

The discrete normalized $L^p$ norm is unchanged by conjugating a function and reflecting its argument: $\|x\mapsto\overline{f(-x)}\|_p=\|f\|_p$.

Translation preserves the discrete normalized $L^p$ norm: for every group element $a$, $\|\tau_a f\|_{p}=\|f\|_{p}$.