Author

D. Norrbo

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Preprint Sep 2026

The essential norm, block sizes, and some Generalized Hilbert operators on lp

We examine the generalized Hilbert (matrix) operators $$ H_{g,\gamma} : (a_n) \mapsto \sum_{n=1}^{\infty} \bigg(\frac{k}{n}\bigg)^{\gamma} \frac{g_k a_n}{n+k} $$ on the $\ell^p$ spaces, $1<p<\infty$, where $g=(g_n)$ is a sequence and $-1/p<\gamma<1-1/p$. Given a partition of the natural numbers $\bigcup_j I_j = \mathbb...

D. Norrbo · 0 citations

Preprint Aug 2026

The Boundedness Problem for Generalized Hilbert Operators on Hardy Spaces

Let $g$ be analytic in the unit disc and consider the generalized Hilbert operator $$ \mathcal{H}_g(f)(z)=\int_0^1 f(t)g'(tz)\, dt. $$ The boundedness of $\mathcal H_g$ on $H^p$ is characterized by the mean Lipschitz condition $g\in\Lambda\left(p,\frac{1}{p}\right)$ when $1<p\leq2$, while the problem remains open for $...

D. Norrbo, J. A. Pel'aez, Fang-Lei Wu · 2 citations · ⚡1

Preprint Sep 2026

Sharp exponential integrability of conjugate functions

We prove that if a real-valued function $f\in L^1$ on the complex unit circle has a gap of width at least $\pi$ in its essential range, then $\exp(\widetilde f)$ is not integrable, where $\widetilde f$ is the conjugate function. More generally, the exponential function can be replaced by any nonnegative convex function...

D. Norrbo, J. Virtanen · 0 citations