Related papers: Analytic version of critical $Q$ spaces and their …

Given two systems $P=(P_j(D))_{j=1}^N$ and $Q=(Q_j(D))_{j=1}^M$ of linear partial differential operators with constant coefficients, we consider the spaces ${\mathcal E}_\omega^P$ and ${\mathcal E}_\omega^Q$ of $\omega$-ultradifferentiable…

Traditional Lp spaces are fundamental in functional analysis, demarcated by the relationship $1/p + 1/q = 1$. This research pioneers the concept of $\theta$-Lebesgue space, stemming from a simultaneous weakening of both the classical $L_p$…

Muthukumar and Ponnusamy \cite{MP-Tp-spaces} studied the multiplication operators on $\mathbb{T}_p$ spaces. In this article, we mainly consider multiplication operators between $\mathbb{T}_p$ and $\mathbb{T}_q$ ($p\neq q$). In particular,…

Let $\alpha,\beta \in \mathbb{R}_{>0}$ be such that $\alpha,\beta$ are quadratic and $\mathbb{Q}(\alpha)\neq \mathbb{Q}(\beta)$. Then every subset of $\mathbb{R}^n$ definable in both $(\mathbb{R},{<},+,\mathbb{Z},x\mapsto \alpha x)$ and…

For $0<p<\infty $ and $\alpha >-1$ the space of Dirichlet type $\mathcal D^p_\alpha $ consists of those functions $f$ which are analytic in the unit disc $\mathbb D$ and satisfy $\int_{\mathbb D}(1-| z| )^\alpha| f^\prime (z)|…

We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations,…

In this paper, the authors define the mixed $\lambda$-central Morrey spaces and the mixed $\lambda$-central $BMO$ spaces. The boundedness of the fractional integral operators $T_{\alpha}$ and its commutators $[b, T_{\alpha}]$ are…

In this paper, we investigate the boundedness and compactness of generalized integration operators $T_g^{n,k}$ and $S_g^{n,0}$ from analytic tent spaces $AT_p^\infty(\alpha)$ to $AT_q^\infty(\beta)$ when $0<p,q<\infty,\alpha,\beta>-2$.

We observe that local embedding problems for certain Hardy and Bergman spaces of Dirichlet series are equivalent to boundedness of a class of composition operators. Following this, we perform a careful study of such composition operators…

The multiplier $\lambda_n$ of a periodic orbit of period $n$ can be viewed as a (multiple-valued) algebraic function on the space of all complex quadratic polynomials $p_c(z)=z^2+c$. We provide a numerical algorithm for computing critical…

To each weighted Dirichlet space $\mathcal{D}_p$, $0<p<1$, we associate a family of Morrey-type spaces ${\mathcal{D}}_p^{\lambda}$, $0< \lambda < 1$, constructed by imposing growth conditions on the norm of hyperbolic translates of…

Let $\mathcal L=-\Delta_{\mathbb H^n}+V$ be a Schr\"odinger operator on the Heisenberg group $\mathbb H^n$, where $\Delta_{\mathbb H^n}$ is the sub-Laplacian on $\mathbb H^n$ and the nonnegative potential $V$ belongs to the reverse H\"older…

This paper provides the foundations of quantum Clifford analysis in $q$-commutative variables with symmetric difference operators. We consider a $q$-Dirac operator on the quantum Euclidean space that factorizes the $U_q(\frak{o})$-invariant…

For an alternate base $\boldsymbol{\beta}=(\beta_0,\ldots,\beta_{p-1})$, we show that if all rational numbers in the unit interval $[0,1)$ have periodic expansions with respect to the $p$ shifts of $\boldsymbol{\beta}$, then the bases…

We study periodic representations in number systems with an algebraic base $\beta$ (not a rational integer). We show that if $\beta$ has no Galois conjugate on the unit circle, then there exists a finite integer alphabet $\mathcal A$ such…

Let $\mathbb{F}$ be a field, let $P \subseteq \mathbb{F}^d$ be a finite set of points, and let $\alpha,\beta \in \mathbb{F} \setminus \{0\}$. We study the quantity \[|\Pi_{\alpha, \beta}| = \{(p,q,r) \in P \times P \times P \mid p \cdot q =…

We study periodic expansions in positional number systems with a base $\beta\in\C,\ |\beta|>1$, and with coefficients in a finite set of digits $\A\subset\C.$ We are interested in determining those algebraic bases for which there exists…

We characterize the (essentially) decreasing sequences of positive numbers $\beta$ = ($\beta$ n) for which all composition operators on H 2 ($\beta$) are bounded, where H 2 ($\beta$) is the space of analytic functions f in the unit disk…

We study partitions of complex numbers as sums of non-negative powers of a fixed algebraic number $\beta$. We prove that if $\beta$ is real quadratic, then the number of partitions is always finite if and only if some conjugate of $\beta$…

We study a reproducing kernel Hilbert space of functions defined on the positive integers and associated to the binomial coefficients. We introduce two transforms, which allow us to develop a related harmonic analysis in this Hilbert space.…