Related papers: Pointwise estimates of weighted Bergman kernels in…

In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we discuss the strong type and weak type estimates for a class of Calder\'on--Zygmund type operators $T_\theta$ in these new weighted spaces. Furthermore, the…

We prove that the norm of a weighted composition operator on the Hardy space H^2 of the disk is controlled by the norm of the weight function in the de Branges-Rovnyak space associated to the symbol of the composition operator. As a…

In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of…

We prove functional inequalities on vector fields on the Euclidean space when it is equipped with a bounded measure that satisfies a Poincar\'e inequality, and study associated self-adjoint operators. The weighted Korn inequality compares…

In this paper, the order boundedness and essential norm of generalized weighted composition operators on Bergman spaces with doubling weights are characterized. Specially, we estimate the essential norm of these operators on weighted…

In this article, we consider Bergman kernels with respect to modules at boundary points, and obtain a log-subharmonicity property of the Bergman kernels, which deduces a concavity property related to the Bergman kernels. As applications, we…

Motivated by the Forelli--Rudin projection theorem we give in this paper a criterion for boundedness of an integral operator on weighted Lebesgue spaces in the interval $(0,1)$. We also calculate the precise norm of this integral operator.…

We give a new proof of correlation estimates for arbitrary moments of the resolvent of random Schr\"odinger operators on the lattice that generalizes and extends the correlation estimate of Minami for the second moment. We apply this moment…

In this paper we continue the study of Bergman theory for the class of slice regular functions. In the slice regular setting there are two possibilities to introduce the Bergman spaces, that are called of the first and of the second kind.…

By using some deep tools from microlocal analysis, the authors of the papers (Ann. of Math., 165 (2007), 567--591, J. Amer. Math. Soc., 23 (2010), 655--691; Invent. Math., 178 (2009), 119--171; Duke Math. J., 158(2011), 83--120) have…

This paper gives embedding theorems for a very general class of weighted Bergman spaces: the results include a number of classical Carleson embedding theorems as special cases. We also consider little Hankel operators on these Bergman…

We solve a long-standing open problem in theory of weighted inequalities concerning iterated Copson operators. We use a constructive approximation method based on a new discretization principle that is developed here. In result, we…

In this paper, we will give the weighted bounds for multilinear fractional maximal type operators $\mathcal{M}_{\Omega,\alpha}$ with rough homogeneous kernels. We obtain a mixed $A_{(\vec{P},q)}-A_\infty$ bound and a $A_{\vec{P}}$ type…

In recent years, it has been well understood that a Calder\'on-Zygmund operator $T$ is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar pointwise…

A method for obtaining complex analytic realizations for a class of deformed algebras based on their respective deformation mappings and their ordinary coherent states is introduced. Explicit results of such realizations are provided for…

We proceed with studying the q-analogues of Cartan domains introduced in q-alg/9703005 and turn to the case of a ball in the space of complex matrices. An explicit expression for a positive $U_q\frak{su}_{nm}$-invariant integral (see…

Pointwise estimates for the gradient of solutions to the $p$-Laplace system with right-hand side in divergence form are established. They enable us to develop a nonlinear counterpart of the classical Calder\'on-Zygmund theory in terms of…

We present a variant of Mourre's commutator theory. We apply it to prove the limiting absorption principle for Schr\"odinger operators with a perturbed Wigner-Von Neumann potential at suitable energies. To our knowledge, this result is new…

Let $L$ be the distinguished Laplacian on the Iwasawa $AN$ group associated with a semisimple Lie group $G$. Assume $F$ is a Borel function on $\mathbb{R}^+$. We give a condition on $F$ such that the kernels of the functions $F(L)$ are…

We completely characterize the boundedness of the area operators from the Bergman spaces $A^p_\alpha(\mathbb{B}_ n)$ to the Lebesgue spaces $L^q(\mathbb{S}_ n)$ for all $0<p,q<\infty$. For the case $n=1$, some partial results were…