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We give an overview of the generalized Calder\'on-Zygmund theory for "non-integral" singular operators, that is, operators without kernels bounds but appropriate off-diagonal estimates. This theory is powerful enough to obtain weighted…
In this paper, we characterize the boundedness and compactness of differences of weighted composition operators from weighted Bergman spaces $A^p_\omega$ induced by a doubling weight $\omega$ to Lebesgue spaces $L^q_\mu$ on the unit ball…
We show that on smooth complete Reinhardt domains, weighted Bergman projection operators corresponding to exponentially decaying weights are unbounded on $L^p$ spaces for all $p\not=2$. On the other hand, we also show that the exponentially…
We consider spectral problems for the Sturm-Liouville operator with arbitrary complex-valued potential q(x) and degenerate boundary conditions. We solve corresponding inverse problem, and also study the completeness property and the basis…
We establish the boundedness of the multilinear Calder\'on-Zygmund operators from a product of weighted Hardy spaces into a weighted Hardy or Lebesgue space. Our results generalize to the weighted setting results obtained by Grafakos and…
In this work, oriented for students with knowledge of basics of linear algebra, we demonstrate, how the use of polar decomposition allows one to understand metric properties of non-degenerate linear operators in $R^2$.
In this paper, we study the local spectral properties of unilateral operator weighted shifts.
All compact $AC(\sigma)$ operators have a representation analogous to that for compact normal operators. As a partial converse we obtain conditions which allow one to construct a large number of such operators. Using the results in the…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
We show that the spectral weights $W_{m\vec K}(\vec k)$ used for the unfolding of two-component spinor eigenstates $| {\psi_{m\vec K}^\mathrm{SC}} > = | \alpha > | {\psi_{m\vec{K}}^\mathrm{SC, \alpha}} > + | \beta > |…
The purpose of this paper is to establish the weighted norm inequalities of one-sided oscillatory integral operators by the aid of interpolation of operators with change of measures.
We obtain a Bloom-type characterization of the two-weighted boundedness of iterated commutators of singular integrals. The necessity is established for a rather wide class of operators, providing a new result even in the unweighted setting…
Weighted shift operators $B$ in space $L^2(X,\mu)$ that are induced by Morse-Smale type of mappings are considered. A description of the properties of $B-\lambda I$ for $\lambda$ belonging to spectrum $\Sigma(B)$ is given. In particular,…
Two proofs of a weighted weak-type $\left(1,\ldots,1;\frac{1}{m}\right)$ estimate for multilinear Calder\'on-Zygmund operators are given. The ideas are motivated by different proofs of the classical weak-type $(1,1)$ estimate for…
This paper studies the behaviour of iterates of weighted composition operators acting on spaces of analytic functions, with particular emphasis on the Hardy space $H^2$. Questions relating to uniform, strong and weak convergence are…
We investigate the decomposability of nonnegative compact r-potent operators on a separable Hilbert space L2(X). We provide a constructive algorithm to prove that basis functions of range spaces of nonnegative r-potent operators can be…
We consider the sl(2)-module structure on the spaces of symbols of differential opera- tors acting on the spaces of weighted densities. We compute the necessary and sufficient integrability conditions of a given infinitesimal deformation of…
In this work we study some general classes of pseudodifferential operators whose symbols are defined in terms of phase space estimates.
The complex scaling method (CSM) provides with a way to obtain resonance parameters of particle unstable states by rotating the coordinates and momenta of the original Hamiltonian. It is convenient to use an L$^2$ integrable basis to…
This paper characterises the boundedness and compactness of Agler--McCarthy monomial operators by reducing them to weighted composition operators and deriving explicit Carleson measure criteria on the half-plane. The results are illustrated…