5 problems

Let $J_H(y)=\boldsymbol{1}_{[-1,1]}(y)y^{-1}$ be the Hilbert transform kernel with a sharp cutoff, and let $\operatorname{Osc}_n(J_H;f)$ denote the corresponding oscillation operat…

Let $d>0$ and let $\beta_d$ be the kernel of the periodic Hilbert transform on the strip of depth $d$, defined for $s\in\mathbb{R}\setminus 2\pi\mathbb{Z}$ by the kernel formulas i…

The NTV conjecture. If $\mathcal{A}_{2}(\sigma,\omega)$ is finite and both testing characteristics $\mathfrak{T}_{H}(\sigma,\omega)$ and $\mathfrak{T}_{H}(\omega,\sigma)$ are finit…

Let $\theta$ be a bounded solution on $[0,T]$ of … where $H$ is the Hilbert transform. The $C^{1/2}$ Hölder seminorm measures the quotient $|\theta(t,x)-\theta(t,y)|/|x-y|^{1/2}$.…

Let … mathbb{R}$. For each interval$I$, define the Poisson integral by … Let$b_I$be the unique, if it \exists, point such that … Let$\widetilde\sigma_I:=\sigma-\sigma{b_I}\del…