arXiv subjects

Mirjana Jovovic

Publications and source records attributed to Mirjana Jovovic.

3 recordsLinked to original sources

arXiv2026

Composition Semigroups on the Besov Spaces

We study semigroups of composition operators acting on the Besov spaces $B_p$, where they exhibit some new behaviors relative to many classical spaces. Often for a Banach space $X$ of analytic functions on the unit disk, the maximal closed space of strong continuity, $[ φ_t, X ]$, exists for every semigroup $\{ φ_t \}$ of analytic self-maps of the disk, and the question whether $[φ_t , X ]$ equals $X$ itself has an answer independent of $\{φ_t\}$. Such is the case for the Hardy and Bergman spaces, Bloch, BMOA, and $H^{\infty}$. For the disk algebra $A$, $[φ_t , A ] = A$ precisely when $\{φ_t\} \subset A$. For $B_p$ with $p \geq 2$, every $\{φ_t\} \subset B_p$ and always $[ φ_t, B_p ] = B_p$, but this fails when $1 < p < 2$. We give an example where $\{φ_t\} \subset B_p$ and yet the induced composition operators $\{C_t\}$ are not bounded on $B_p$ and we do not know if $[φ_t,B_p]$ exists. If it does exist, it cannot be equal to $B_p$. Under the hypothesis that there is a uniform bound for the operator norms of the $\{C_t\}$, $0 \leq t \leq 1$, we characterize the semigroups $\{ φ_t \}$ such that $[ φ_t, B_p ] = B_p$.

math.FA↗

arXiv2026

Composition Semigroups on BMOA and $H^{\infty}$

We study $[ϕ_t , X]$, the maximal space of strong continuity for a semigroup of composition operators induced by a semigroup $\{ϕ_t\}_{t\ge0}$ of analytic self-maps of the unit disk, when $X$ is BMOA, $H^\infty$ or the disk algebra. In particular, we show that $[ϕ_t,\text{BMOA}] \neq \text{BMOA}$ for all nontrivial semigroups. We also prove, for every semigroup $\{ϕ_t\}_{t\ge0}$, that $\lim_{t \to 0^+} ϕ_t(z) = z$ not just pointwise, but in $H^{\infty}$ norm. This provides a unified proof of known results about $[ϕ_t , X]$ when $X \in \{H^p, A^p, \mathcal B_0, \text{VMOA}\}$.

math.FA↗

arXiv2024

Some integral operators acting on $H^{\infty}$

Let $f$ and $g$ be analytic on the unit disc $\mathbb{D}$. The integral operator $T_g$ is defined by $ T_g f(z) = \int_0^z f(t)g'(t)\,dt$, $z \in \mathbb{D}$. The problem considered is characterizing those symbols $g$ for which $T_g$ acting on $H^\infty$, the space of bounded analytic functions on $\mathbb{D}$, is bounded or compact. When the symbol is univalent, these become questions in univalent function theory. The corresponding problems for the companion operator, $ S_g f(z)= \int_0^z f'(t)g(t)\, dt$, acting on $H^\infty$ are also studied.

math.CV↗