Related papers: On Harmonic Noncommutative $L^p$-Operators on Loca…

We obtain a complete characterization of the weak-type $(1,1)$ for Haar shift operators in terms of generalized Haar systems adapted to a Borel measure $\mu$ in the operator-valued setting. The main technical tool in our method is a…

Boundedness and compactness properties of multiplication operators on quantum (non-commutative) function spaces are investigated. For endomorphic multiplication operators these properties can be characterized in the setting of quantum…

Let $(X, d, \mu)$ be a space of homogeneous type, i.e. the measure $\mu$ satisfies doubling (volume) property with respect to the balls defined by the metric $d$. Let $L$ be a non-negative self-adjoint operator on $L^2(X)$. Assume that the…

We establish a modified pointwise convex body domination for vector-valued Haar shifts in the nonhomogeneous setting, strengthening and extending the scalar case developed in arXiv:2309.13943. Moreover, we identify a subclass of shifts,…

It is known that, for a positive Dunford-Schwartz operator in a noncommutative $L^p-$space, $1\leq p<\infty$ or, more generally, in a noncommutative Orlicz space with order continuous norm, the corresponding ergodic averages converge…

We prove $\mathrm{H}^1$ and $\mathrm{BMO}$ endpoint inequalities for generic cancellative Haar shifts defined with respect to a possibly non-homogeneous Borel measure $\mu$ satisfying a weak regularity condition. This immediately yields a…

We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions which was recently studied as a vector space by Rosas and Sagan. The bases for this algebra are indexed by set partitions. We show that there…

In 2008, Blecher and Labuschagne extended Beurling's classical theorem to $H^\infty$-invariant subspaces of $L^p(\mathcal{M},\tau)$ for a finite von Neumann algebra $\mathcal{M}$ with a finite, faithful, normal tracial state $\tau$ when…

It is well known that if $G/K$ is any irreducible symmetric space and $\mu _{a}$ is a continuous orbital measure supported on the double coset $KaK,$ then the convolution product, $\mu _{a}^{k},$ is absolutely continuous for some suitably…

We study the twisted-Hopf-algebra symmetries of observer-independent canonical spacetime noncommutativity, for which the commutators of the spacetime coordinates take the form [x^{mu},x^{nu}]=i theta^{mu nu} with observer-independent (and…

In this paper, we investigate the compactness of the commutator $[C_\psi^{\ast}, C_\varphi]$ on the Hardy space $H^2(B_N)$ or the weighted Bergman space $A^2_s(B_N)$ ($s>-1$), when $\varphi$ and $\psi$ are automorphisms of the unit ball…

This paper seeks to extend the theory of composition operators on analytic functional Hilbert spaces from analytic symbols to quasiconformal ones. The focus is the boundedness but operator-theoretic questions are discussed as well. In…

We present a generalization of Hirschman's entropic uncertainty principle for locally compact abelian groups to unimodular locally compact quantum groups. As a corollary, we strengthen a well-known uncertainty principle for compact groups,…

We give a proof of the Khintchine inequalities in non-commutative $L_p$-spaces for all $0< p<1$. These new inequalities are valid for the Rademacher functions or Gaussian random variables, but also for more general sequences, e.g. for the…

Let $G$ be a reductive group in the Harish-Chandra class e.g. a connected semisimple Lie group with finite center, or the group of real points of a connected reductive algebraic group defined over $\R$. Let $\sigma$ be an involution of the…

We extend the decomposition conjecture to 2d quantum field theories with a gauged $\text{Rep}(H)$ symmetry category for $H$ a finite-dimensional semisimple Hopf algebra with $\text{Rep}(G)$ trivially-acting and $\text{Vec}(\Gamma)$ the…

We derive a necessary condition for compactness of the weighted $\overline\partial$-Neumann operator on the space $L^2(\mathbb C^n,e^{-\varphi})$, under the assumption that the corresponding weighted Bergman space of entire functions has…

We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces $H^\Psi$: construction of a "slow" Blaschke product giving a non-compact composition operator on $H^\Psi$;…

In this paper, we investigate the complex symmetric structure of generalized weighted composition operators $D_{m,\psi,\varphi}$ on the weighted Hardy space $H^2(\beta)$. We obtain explicit conditions for $ D_{m,\psi,\varphi}$ to be complex…

As our main result, we supply the missing characterization of the $L^p(\mu)\to L^q(\lambda)$ boundedness of the commutator of a non-degenerate Calder\'on--Zygmund operator $T$ and pointwise multiplication by $b$ for exponents $1<q<p<\infty$…