相关论文: Commutators of singular integrals on generalized $…

In a previous paper, we introduced a new class of Gaussian singular integrals, that we called the general alternative Gaussian singular integrals and study the boundedness of them on $L^p(\gamma_d)$, $ 1 < p < \infty.$ In this paper, we…

In this paper, we establish the boundedness of the commutators of multilinear Hausdorff operators on the product of some weighted Morrey-Herz type spaces with variable exponent with their symbols belong to both Lipschitz space and central…

A classification of weakly compact multiplication operators on L(L_p), $1<p<\infty$, is given. This answers a question raised by Saksman and Tylli in 1992. The classification involves the concept of $\ell_p$-strictly singular operators, and…

In this paper, the central BMO spaces with variable exponent are introduced. As an application, we characterize these spaces by the boundedness of commutators of Hardy operator and its dual operator on variable Lebesgue spaces. The…

Given $1\leq q<p<\infty$ quantitative weighted L^p estimates, in terms of Aq weights, for vector valued maximal functions, Calder\'on-Zygmund operators, commutators and maximal rough singular integrals are obtained. The results for singular…

It is shown that product BMO of Chang and Fefferman, defined on the product of Euclidean spaces can be characterized by the multiparameter commutators of Riesz transforms. This extends a classical one-parameter result of Coifman, Rochberg,…

We consider Aichinger's equation $$f(x_1+\cdots+x_{m+1})=\sum_{i=1}^{m+1}g_i(x_1,x_2,\cdots, \widehat{x_i},\cdots, x_{m+1})$$ for functions defined on commutative semigroups which take values on commutative groups. The solutions of this…

We consider the Casimir Invariants related to some a special kind of Lie-algebra extensions, called universal extensions. We show that these invariants can be studied using the equivalence between the universal extensions and the…

We deal with the boundedness properties of higher order commutators related to some generalizations of the multilinear fractional integral operator of order $m$, $I_\alpha ^m$, from a product of weighted Lebesgue spaces into adequate…

We construct quantum commutators on module-algebras of quasi-triangular Hopf algebras. These are quantum-group covariant, and have generalized antisymmetry and Leibniz properties. If the Hopf algebra is triangular they additionally satisfy…

Let $p$ be a prime number. Motivated by the local lifting problem for $(\mathbb{Z}/p\mathbb{Z})^n$ with $n>1$, we prove several new results on certain $\mathbb{F}_p$-vector spaces of logarithmic differential forms on the projective line in…

In this paper the asymmetric generalization of the Glazman-Povzner-Wienholtz theorem is proved for one-dimensional Schr\"{o}dinger operators with strongly singular matrix potentials from the space $H_{loc}^{-1}(\mathbb{R},…

Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ for all $\tilde w\in A_{p_1}(\mathbb R^d)$ and in addition compact on $L^{p_1}(w_1)$ for some $w_1\in A_{p_1}(\mathbb R^d)$. Then $T$ is…

We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including $L^p$-$L^q$, $L^p$-$BMO$ and $L^p$-Lipschitz estimates. The kernels of such operators satisfy…

Every unital nonselfadjoint operator algebra possesses canonical and functorial classes of faithful (even completely isometric) Hilbert space representations satisfying a double commutant theorem generalizing von Neumann's classical result.…

In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…

The operators on $\LP=L_p[0,1]$, $1\leq p<\infty$, which are not commutators are those of the form $\lambda I + S$ where $\lambda\neq 0$ and $S$ belongs to the largest ideal in $\opLP$. The proof involves new structural results for…

Let $F/\mathbb{Q}_p$ be a finite extension. We explore the universal supersingular mod $p$ representations of $\mathrm{GL}_2(F)$ through computing a basis of their invariant space under the pro-$p$ Iwahori subgroup. This generalizes works…

We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of…

For the algebra L= K <x, d/dx, \int> of polynomial integro-differential operators over a field K of characteristic zero, a classification of indecomposable, generalized weight L-modules of finite length is given. Each such module is an…