Searcharxiv⌕ Search

arXiv subjects

Nikolaos Chalmoukis

Publications and source records attributed to Nikolaos Chalmoukis.

At least 19 recordsLinked to original sources
arXiv2026

Quaternionic Carleson measures

In this paper we provide a general construction of a quaternionic Banach space of slice regular functions from a given Banach space of holomorphic functions, which we call its quaternionic lift. To the best of our knowledge, this construction encompasses all known examples of quaternionic Banach spaces of slice regular functions in the literature. Our main result is a characterization of Carleson and vanishing Carleson measures for such quaternionic Banach function spaces in terms of the corresponding Carleson measures of the underlying holomorphic function space. This offers a unified approach to a problem that so far has been treated on a case-by-case basis.

math.FA↗
arXiv2026

Generalized Foguel-Hankel Operators

In this paper we introduce a more general class of Foguel-Hankel operators, where the unilateral shift on $\ell^2(\mathbb{N}) $ is replaced by a general multiplication operator on the Hardy space $H^2$ . We prove that Peller's condition is sufficient for the operator to be power bounded, but in general it is not necessary. When the Hankel matrix is the Hilbert matrix, we prove that being similar to a contraction is equivalent to the (a priori) weaker Kreiss condition.

math.FA↗
arXiv2026

Discrete random Clark measures and associated inner functions

We study a class of random inner functions $φ$ whose Clark measure at $1$ is the weighted sum of point masses supported on independent uniformly distributed points of $\mathbb T$. Our first result shows that $φ$ is almost surely a Blaschke product. We then investigate when $φ$ admits angular derivative almost surely and we provide a $0 - 1$ law. These conditions have a direct interpretation in terms of the other Clark measures associated with $φ$. Finally, we obtain quantitative estimates for the zeros of $φ$, proving that, in suitable regimes, their distribution satisfies summability conditions stronger than the classical Blaschke condition.

math.CV↗
arXiv2026

Uncentred maximal operators with respect to half balls on Damek--Ricci spaces

In this paper we study a variant of the uncentred Hardy--Littlewood maximal operator on Damek--Ricci spaces in which balls are replaced by suitable half balls. Perhaps surprisingly, such modified maximal operator has better boundedness properties than the classical one. In particular, it is bounded on $L^p$ for every $p$ in $(1,\infty]$ (whereas the analogue operator on balls is bounded on $L^p$ only for $p>2$), and satisfies a limiting distributional inequality if $f$ is in $L\log (2+L)$. This endpoint estimate is optimal in the sense that it does not hold if $L\log ({2}+L)$ is replaced by a larger (in a suitable sense) Orlicz space.

math.FA↗
arXiv2026

Operators with small Kreiss constants

We investigate matrices satisfying the Kreiss condition $$\|(zI-T)^{-1}\|\le\cfrac{K}{|z|-1}, \hspace{0.7 cm} |z|>1, $$ with $K$ lying arbitrarily close to $1.$ We provide lower bounds for the power growth of such matrices, which complement and refine related estimates due to Nikolski and Spijker-Tracogna-Welfert. We also study operators that satisfy a variant of the above Kreiss condition where $K$ is replaced by $1+ε(|z|)$, where the positive continuous function $ε(|z|)$ tends to $0$ as $|z|\to 1^+.$ We show that, if the spectrum of $T$ touches the unit circle only at a single point and the resolvent of $T$ satisfies a growth restriction along the unit circle, it is possible to choose $ε$ so that this Kreiss-type condition guarantees similarity to a contraction. At the core of our proof lies a positivity argument involving the double-layer potential operator. Counterexamples related to less restrictive choices of $ε$ are also provided.

math.FA↗
arXiv2026

Maximal subspaces of strong continuity for composition semigroups

Let $(φ_t)_{t\geq 0} $ a semigroup of holomorphic self-maps of the unit disk and $C_t f = f \circ φ_t $ the semigroup of composition operators which corresponds to $φ_t. $ Given a non-separable Banach space of analytic functions $X $ we study the properties of the maximal subspace of $X $ on which the semigroup $C_t $ is strongly continuous. In particular when $X $ contains the polynomials an interesting question is for which semigroups the maximal subspace of strong continuity coincides with the norm closure of the polynomials. This problem has been investigated in several function spaces including $BMOA$, $BMOA_p $, the Bloch space, $Q_s $ space and analytic Morrey spaces. However, in most cases only partial results are available. We offer a unified approach to this problem which encompasses all of the above spaces as particular examples. Moreover, we completely characterize the semigroups for which the maximal subspace of strong continuity coincides with the norm-closure of the polynomials in the space, giving therefore sharp versions of a number of results in the literature.

math.FA↗
arXiv2025

Simply interpolating and Carleson sequences for Hardy spaces in the polydisc

We study the relation between simply and universally interpolating sequences for the holomorphic Hardy spaces $H^p(\mathbb{D}^d)$ on the polydisc. In dimension $d=1$ a sequence is simply interpolating if and only if it is universally interpolating, due to a classical theorem of Shapiro and Shields. In dimension $d\ge2$, Amar showed that Shapiro and Shields' theorem holds for $H^p(\mathbb{D}^d)$ when $p \geq 4$. In contrast, we show that if $1\leq p \leq 2$ there exist simply interpolating sequences which are not universally interpolating.

math.FA↗
arXiv2025

Spider's webs and sharp $L^p$ bounds for the Hardy--Littlewood maximal operator on Gromov hyperbolic spaces

In this paper we prove that if $1 τ$, and it is of weak type $(τ,τ)$, where $τ:= \log_ab$. A key step in the proof is a new structural theorem for Gromov hyperbolic spaces with $(a,b)$-pinched exponential growth at infinity, consisting in a discretisation of $X$ by means of certain graphs, introduced in this paper and called spider's webs, with ``good connectivity properties". Our result applies to trees with bounded geometry, and Cartan--Hadamard manifolds of pinched negative curvature, providing new boundedness results in these settings. The index $τ$ is optimal in the sense that if $p<τ$, then there exists $X$ satisfying the assumptions above such that $\mathcal M$ is not of weak type $(p,p)$. Furthermore, if $b>a^2$, then there are examples of spaces $X$ satisfying the assumptions above such that $\mathcal M$ bounded on $L^p(X)$ if and only if $p=\infty$.

math.FA↗
arXiv2024

Potential theory and boundary behavior in the Drury-Arveson space

We develop a notion of capacity for the Drury-Arveson space $H^2_d$ of holomorphic functions on the Euclidean unit ball. We show that every function in $H^2_d$ has a non-tangential limit (in fact Korányi limit) at every point in the sphere outside of a set of capacity zero. Moreover, we prove that the capacity zero condition is sharp, and that it is equivalent to being totally null for $H^2_d$. We also provide applications to cyclicity. Finally, we discuss generalizations of these results to other function spaces on the ball.

math.FA↗
arXiv2024

Random Carleson Sequences for the Hardy space on the Polydisc and the Unit Ball

We study the Kolmogorov 0-1 law for a random sequence with prescribed radii so that it generates a Carleson measure almost surely, both for the Hardy space on the polydisc and the Hardy space on the unit ball, thus providing improved versions of previous results of the first two authors and of a separate result of Massaneda. In the polydisc, the geometry of such sequences is not well understood, so we proceed by studying the random Gramians generated by random sequences, using tools from the theory of random matrices. Another result we prove, and that is of its own relevance, is the 0-1 law for a random sequence to be partitioned into M separated sequences with respect to the pseudo-hyperbolic distance, which is used also to describe the random sequences that are interpolating for the Bloch space on the unit disc almost surely.

math.CV↗
arXiv2024

On the boundedness of generalized integration operators on Hardy spaces

We study the boundedness and compactness properties of the generalized integration operator $T_{g,a}$ when it acts between distinct Hardy spaces in the unit disc of the complex plane. This operator has been introduced by the first author in connection to a theorem of Cohn about factorization of higher order derivatives of functions in Hardy spaces. We answer in the affirmative a conjecture stated in the same work, therefore giving a complete characterization of the class of symbols $g$ for which the operator is bounded from the Hardy space $H^p$ to $H^q, \, 0<p,q<\infty.$

math.CV↗
arXiv2024

Generalized Hilbert operators arising from Hausdorff matrices

For a finite, positive, Borel measure $μ$ on $(0,1)$ we consider an infinite matrix $Γ_μ$, related to the classical Hausdorff matrix defined by the same measure $μ$, in the same algebraic way that the Hilbert matrix is related to the Cesáro matrix. When $μ$ is the Lebesgue measure, $Γ_μ$ reduces to the classical Hilbert matrix. We prove that the matrices $Γ_μ$ are not Hankel, unless $μ$ is a constant multiple of the Lebesgue measure, we give necessary and sufficient conditions for their boundedness on the scale of Hardy spaces $H^p, \, 1 \leq p < \infty$, and we study their compactness and complete continuity properties. In the case $2\leq p<\infty$, we are able to compute the exact value of the norm of the operator.

math.FA↗
arXiv2023

On the speed of convergence in the ergodic theorem for shift operators

Given a probability space $(X,μ)$, a square integrable function $f$ on such space and a (unilateral or bilateral) shift operator $T$, we prove under suitable assumptions that the ergodic means $N^{-1}\sum_{n=0}^{N-1} T^nf$ converge pointwise almost everywhere to zero with a speed of convergence which, up to a small logarithmic transgression, is essentially of the order of $N^{-1/2}$. We also provide a few applications of our results, especially in the case of shifts associated with toral endomorphisms.

math.CA↗
arXiv2023

Simply interpolating sequences in complete Pick spaces

We characterize simply interpolating sequences (also known as onto interpolating sequences) for complete Pick spaces. We show that a sequence is simply interpolating if and only if it is strongly separated. This answers a question of Agler and McCarthy. Moreover, we show that in many important examples of complete Pick spaces, including weighted Dirichlet spaces on the unit disc and the Drury-Arveson space in finitely many variables, simple interpolation does not imply multiplier interpolation. In fact, in those spaces, we construct simply interpolating sequences that generate infinite measures, and uniformly separated sequences that are not multiplier interpolating.

math.FA↗
arXiv2022

A note on simply interpolating sequences for the Dirichlet space

We study simply interpolating sequences for the Dirichlet space in the unit disc. In particular we are interested in comparing three different sufficient conditions for simply interpolating sequences. The first one is the the so called one box condition, the second is the column bounded propererty for the associated Grammian matrix and the third one is a restricted version of the one box condition introduced by Bishop and, independently, by Marshall and Sundberg. We prove that the one box condition implies the column bounded property which in turn implies the restricted on box condition of Bishop-Marshall-Sundberg, and we give two counterexamples which show that the reverse implications fail even for weakly separated sequences.

math.CV↗
arXiv2022

Totally null sets and capacity in Dirichlet type spaces

In the context of Dirichlet type spaces on the unit ball of $\mathbb{C}^d$, also known as Hardy-Sobolev or Besov-Sobolev spaces, we compare two notions of smallness for compact subsets of the unit sphere. We show that the functional analytic notion of being totally null agrees with the potential theoretic notion of having capacity zero. In particular, this applies to the classical Dirichlet space on the unit disc and logarithmic capacity. In combination with a peak interpolation result of Davidson and the second named author, we obtain strengthenings of boundary interpolation theorems of Peller and Khrushchëv and of Cohn and Verbitsky.

math.FA↗
arXiv2022

Two-weight dyadic Hardy's inequalities

We present various results concerning the two-weight Hardy's inequality on infinite trees. Our main scope is to survey known characterizations (and proofs) for trace measures, as well as to provide some new ones. Also for some of the known characterizations we provide here new proofs. In particular, we obtain a new characterization based on a new reverse Hölder inequality for trace measures, and one based on the well known Muckenhoupt-Wheeden-Wolff inequality, of which we here give a new probabilistic proof. We provide a new direct proof for the so called isocapacitary characterization and a new simple proof, based on a monotonicity argument, for the so called mass-energy characterization. Furthermore, we introduce a conformally invariant version of the two-weight Hardy's inequality, we characterize the compactness of the Hardy operator, we provide a list of open problems and suggest some possible lines of future research.

math.CA↗