Related papers: Commutators, paraproducts and BMO in non-homogeneo…
\'O. Blasco and S. Pott showed that the supremum of operator norms over $L^2$ of all bicommutators (with the same symbol) of one-parameter Haar multipliers dominates the biparameter dyadic product BMO norm of the symbol itself. In the…
In this paper, we consider partial sums of triangular martingale differences weighted by random variables drawn uniformly on the sphere, and globally independent of the martingale differences. Starting from the so-called principle of…
Representations by linear integral operators on $L_p$ spaces over measure spaces are investigated for the polynomial covariance type commutation relations and more general two-sided generalizations of covariance commutation relations…
The comparison of the Hamiltonians of the noncommutative isotropic harmonic oscillator and Landau problem are analysed to study the specific conditions under which these two models are indistinguishable. The energy eigenvalues and…
This note is devoted to establishing two-weight estimates for commutators of singular integrals. We combine multilinearity with product spaces. A new type of two-weight extrapolation result is used to yield the quasi-Banach range of…
We study Bessel processes on Weyl chambers of types A and B on $\mathbb R^N$. Using elementary symmetric functions, we present several space-time-harmonic functions and thus martingales for these processes $(X_t)_{t\ge0}$ which are…
We investigate the effects of noncommutativity between the position-position, position-momentum and momentum-momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such noncommutativity…
We investigate parabolic Muckenhoupt weights and functions of bounded mean oscillation (BMO) related to nonlinear parabolic partial differential equations. The main result gives a full characterization of weak and strong type weighted norm…
Non-commutative propositions are characteristic of both quantum and non-quantum (sociological, biological, psychological) situations. In a Hilbert space model states, understood as correlations between all the possible propositions, are…
We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with aconstant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter,…
Let $(X,d,\mu)$ be a non-homogeneous metric measure space satisfying both the geometrically doubling and the upper doubling measure conditions. In this paper, the boundedness of multilinear fractional integral operator in this setting is…
It has been pointed out that different choices of momenta can be associated to the same noncommutative spacetime model. The question of whether these momentum spaces, related by diffeomorphisms, produce the same physical predictions is…
In this work we establish an BDG inequality type for certain nonlinear martingale arizing from BSDE.
Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2(R^n)$ with Gaussican kernel bounds, and let $L^{-\alpha/2}$ be the fractional integrals of $L$ for $0<\alpha<n.$ For any locally integrable function $b$, The…
By viewing non-commutative polynomials, that is, elements in free associative algebras, in terms of linear representations, we generalize Horner's rule to the non-commutative (multivariate) setting. We introduce the concept of Horner…
Motivated by the recent work on asymptotic independence relations for random matrices with non-commutative entries, we investigate the limit distribution and independence relations for large matrices with identically distributed and Boolean…
In this article, we will define non-commutative covering spaces using Hopf-Galois theory. We will look at basic properties of covering spaces that still hold for these non-commutative analogues. We will describe examples including coverings…
This paper examines various kinds of subspaces of the non-commutative spaces that are modelled on quasi-projective commutative schemes. It is shown how intersections and unions of weakly closed subspaces, closed subspaces, their weakly open…
Following the guidelines of classical differential geometry the `building material' for the tensor calculus in non-commutative geometry is suggested. The algebraic account of moduli of vectors and covectors is carried out.
We express classical, free, Boolean and monotone cumulants in terms of each other, using combinatorics of heaps, pyramids, Tutte polynomials and permutations. We completely determine the coefficients of these formulas with the exception of…