Related papers: A noncommutative Davis' decomposition for martinga…

Given a quiver algebra A with relations defined by a superpotential, this paper defines a set of invariants of A counting framed cyclic A-modules, analogous to rank-1 Donaldson-Thomas invariants of Calabi-Yau threefolds. For the special…

In this paper we characterize for 0 < p \leq \infty, the closed subspaces of Hp that are invariant under multiplication by all powers of a finite Blaschke factor B, except the first power. Our result clearly generalizes the invariant…

In the first part of this study we consider the boundedness and compactness properties of Cauchy-Fantappie type operators on Poletsky-Stessin Hardy spaces $H^{p}_{u}(\mathbb{B}^{\textbf{p}})$ of complex ellipsoids. We show that boundedness…

A non-commutative differential calculus on the $h$-superplane is presented via a contraction of the $q$-superplane. An R-matrix which satisfies both ungraded and graded Yang-Baxter equations is obtained and a new deformation of the $(1+1)$…

This paper is devoted to the study of various maximal ergodic theorems in noncommutative $L_p$-spaces. In particular, we prove the noncommutative analogue of the classical Dunford-Schwartz maximal ergodic inequality for positive…

In this work we extend the theory of the classical Hardy space $H^1$ to the rational Dunkl setting. Specifically, let $\Delta$ be the Dunkl Laplacian on a Euclidean space $\mathbb{R}^N$. On the half-space $\mathbb{R}_+\times\mathbb{R}^N$,…

Let $1\le p<\8$ and $(x_n)_{\nen}$ be a sequence of positive elements in a non-commutative $L_p$ space and $(E_n)_{\nen}$ be an increasing sequence of conditional expectations, then the $L_p$ norm of \sum_n E_n(x_n) can be estimated by c_p…

We show that the space of all bounded derivations from the disc algebra into its dual can be identified with the Hardy space $H^1$; using this, we infer that all such derivations are compact. Also, given a fixed derivation $D$, we construct…

We give an alternative proof of a Marcinkiewicz interpolation theorem for non commutative maximal functions and positive maps, slightly refining earlier versions of the statement. The main novelty is that it provides a substitute for the…

We give a simple and natural proof for the compatibility of the Hasse invariant with duality. We then study a $p$-divisible group with an action of the ring of integers of a finite ramified extension of $\mathbb{Q}_p$. We suppose that it…

We prove an $l^p$ decoupling inequality for hypersurfaces with nonzero Gaussian curvature and use it to derive a corresponding $l^p$ decoupling for curves not contained in a hyperplane. This extends our earlier work from [2]

Classical and quantum mechanics for an extended Heisenberg algebra with canonical commutation relations for position and momentum coordinates are considered. In this approach additional noncommutativity is removed from the algebra by linear…

In this paper, we prove the Hardy-Leray inequality and related inequalities in variable Lebesgue spaces. Our proof is based on a version of the Stein-Weiss inequality in variable Lebesgue spaces derived from two weight inequalities due to…

We obtain Fourier inequalities in the weighted $L_p$ spaces for any $1<p<\infty$ involving the Hardy-Ces\`aro and Hardy-Bellman operators. We extend these results to product Hardy spaces for $p\le 1$. Moreover, boundedness of the…

We continue our development of a new basis for the algebra of non-commutative symmetric functions. This basis is analogous to the Schur basis for the algebra of symmetric functions, and it shares many of its wonderful properties. For…

This article is devoted to the noncommutative version of the Laplace transformation. New types of the direct and inverse transformations of the Laplace type over general Cayley-Dickson algebras, in particular, also the skew field of…

As a first step at developing a theory of noncommutative nonlinear elliptic partial differential equations, we analyze noncommutative analogues of Laplace's equation and its variants (some of the them nonlinear) over noncommutative tori.…

Recently the author proved that the 1977 Hummel-Scheinberg-Zalcman conjecture on coefficients of nonvanishing $H^p$ functions is true for all $p = 2m, m \in \mathbb{N}$, i.e., for the Hilbertian Hardy spaces $H^{2m}$. As a consequence, this…

We equip a family of algebras whose noncommutativity is of Lie type with a derivation based differential calculus obtained, upon suitably using both inner and outer derivations, as a reduction of a redundant calculus over the Moyal four…

We prove that if X is a separable, reflexive space which is asymptotic l_p, then X embeds into a reflexive space Z having an asymptotic l_p finite-dimensional decomposition. This result leads to an intrinsic characterization of subspaces of…