Related papers: Bj\"ork-Sj\"olin condition for strongly singular c…
We study a specific class of Fourier integral operators characterized by symbols belonging to the multi-parameter H\"ormander class $\mathbf{S}^m(\R^{ n_1} \times \R^{ n_2} \times \cdots \times \R^{n_d} )$, where $n= n_1 + n_2 +\cdots +…
Supplying the missing necessary conditions, we complete the characterisation of the $L^p\to L^q$ boundedness of commutators $[b,T]$ of pointwise multiplication and Calder\'on-Zygmund operators, for arbitrary pairs of $1<p,q<\infty$ and…
We complement the recent theory of general singular integrals $T$ invariant under the Zygmund dilations $(x_1, x_2, x_3) \mapsto (s x_1, tx_2, st x_3)$ by proving necessary and sufficient conditions for the boundedness and compactness of…
This paper develops some deeper consequences of an extended definition, proposed previously by the author, of pseudo-differential operators that are of type $1,1$ in H\"ormander's sense. Thus, it contributes to the long-standing problem of…
The paper concerns upper and lower estimates for the number of negative eigenvalues of one- and two-dimensional Schr\"{o}dinger operators and more general operators with the spectral dimensions $d\leq 2$. The classical Cwikel-Lieb-Rosenblum…
We study mixed weak type inequalities for the commutator $[b,T]$, where $b$ is a BMO function and $T$ is a Calder\'on-Zygmund operator. More precisely, we prove that for every $t>0$ \begin{equation*}%\label{tesis_teo2.2} uv(\{x\in\R^n:…
We consider Schr\"odinger operators with potentials satisfying a generalized bounded variation condition at infinity and an $L^p$ decay condition. This class of potentials includes slowly decaying Wigner--von Neumann type potentials…
In the present paper, we establish that Riesz transforms for Dunkl Hermite expansion as introduced in [4] are singular integral operators with H\"ormander's type conditions and we show that are bounded on $L^p(\mathbb{R}^d; d\mu_k) 1 < p <…
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…
The evolution of mixed states of a closed quantum system is described by a group of evolution superoperators whose infinitesimal generator (the quantum Liouville superoperator, or Liouvillian) determines the mixed-state counterpart of the…
We present a new necessary condition for similarity of indefinite Sturm-Liouville operators to self-adjoint operators. This condition is formulated in terms of Weyl-Titchmarsh $m$-functions. Also we obtain necessary conditions for…
For a time-dependent harmonic oscillator with an inverse squared singular term, we find the generalized invariant using the Lie algebra of $SU(2)$ and construct the number-type eigenstates and the coherent states using the…
We first consider two types of localizations of singular integral operators of convolution type, and show, under mild decay and smoothness conditions on the auxiliary functions, that their boundedness on the local Hardy space…
We provide a study of the Riesz transforms on stratified nilpotent Lie groups, and obtain a certain version of the pointwise lower bound of the Riesz transform kernel. Then we establish the characterisation of the BMO space on stratified…
We define an involution on the space of elliptic unipotent Langlands parameters of a reductive $p$-adic group $G$ and verify that when $G$ is split adjoint exceptional, the composition of this involution with the hyperspecial parahoric…
Quantum harmonic analysis on phase space is shown to be linked with localization operators. The convolution between operators and the convolution between a function and an operator provide a conceptual framework for the theory of…
A Markov operator $P$ on a $\sigma$-finite measure space $(X, \Sigma, m)$ with invariant measure $m$ is said to have Krengel-Lin decomposition if $L^2 (X) = E_0 \oplus L^2 (X,\Sigma_d)$ where $E_0 = \{f \in L^2 (X) \mid ||P^n (f) || \ra 0…
In this paper, the index groups for which the weighted Young's inequalities hold in both continuous case and discrete case are characterized. As applications, the index groups for the product inequalities on modulation spaces are…
In this paper we obtain the weak type (1,1) boundedness of Calderon-Zygmund operators acting over operator-valued functions. Our main tools for its solution are a noncommutative form of Calderon-Zygmund decomposition in conjunction with a…
The main theme of this paper is to give sufficient conditions for the weighted boundedness of the bilinear fractional integral operator $\mathsf{BI}_\al$. The proposed condition involves the union of multilinear Muckenhoupt-type conditions.…