Research proof index

The Marcinkiewicz-Zygmund inequality for real-valued functions, with a slightly better constant than Real.marcinkiewicz_zygmund.

For any function F : ℍ → ℂ and t > 0, F.resToImagAxis (1/t) = F(S • (I*t)).

Real part of a product on the imaginary axis is the product of real parts, when both factors are real-valued there.

Restriction and slash action under S: $(F |_k S) (it) = (it)^{-k} * F(it)$

If $f$ is integrable on the open annulus $\{y:R_1<d(x,y)<R_2\}$, then varying the inner radius from the right changes the annular integral continuously at $R_1$:

$R\longmapsto\int_{R<d(x,y)<R_2}f(y)\,dy$

is right-continuous at $R=R_1$.

Rudin's inequality, exponential form.