Related papers: New estimates for bounded oscillation operators
Let $\mu$ be an $n$-dimensional finite positive measure on $\mathbb{R}^m$. We obtain a $T1$ condition sufficient for the boundedness of Calder\'{o}n-Zygmund operators on $\textrm{RBMO}(\mu)$, the regular BMO space of Tolsa.
This work establishes new results on spectral theory and time evolution for matrix-valued discrete Schr\"odinger operators on the space of square-summable matrix sequences. The matrix-valued formalism is employed to streamline notation,…
The classical Littlewood's theorem establishes boundedness and provides a norm estimate for composition operators on the Hardy space. In this paper, we offer an alternative proof of boundedness and derive a new norm estimate that improves…
In this paper we establish a T1 criterion for the boundedness of Hermite-Calderon-Zygmund operators on the BMO_H(R^n) space naturally associated to the Hermite operator H. We apply this criterion in a systematic way to prove the boundedness…
In this paper, we give a characterization of mixed $\lambda$-central bounded mean oscillation space $\mathrm{CBMO}^{\vec{q},\lambda}(\mathbb{R}^{n})$ via the boundedness of the commutators of $n$-dimensional Hardy operator $\mathcal{H}$ and…
We prove the boundedness of a trilinear operator that is modulation invariant and which contains curvature information given by the presence of a complex exponential, adding to the small class of examples of such operators.
In this paper, the main aim is to demonstrate the boundedness for commutators of (fractional) maximal function and sharp maximal function in the slice spaces, where the symbols of the commutators belong to the BMO space, whereby some new…
Let $\delta\in(0,1]$ and $T$ be a $\delta$-Calder\'on-Zygmund operator. Let $w$ be in the Muckenhoupt class $A_{1+\delta/n}({\mathbb R}^n)$ satisfying $\int_{{\mathbb R}^n}\frac {w(x)}{1+|x|^n}\,dx<\infty$. When $b\in{\rm BMO}(\mathbb…
In this paper, we will introduce a new notion, that of $K$-Integral operator frames in the set of all bounded linear operators noted $\mathcal{B}(H)$, where $H$ is a separable Hilbert space. Also, we prove some results of integral…
In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…
We establish quantitative upper and lower bounds for Schr\"odinger operators with complex potentials that satisfy some weak form of sparsity. Our first result is a quantitative version of an example, due to S.\ Boegli (Comm. Math. Phys.,…
We consider bilinear oscillatory integrals, i.e. pseudo-product operators whose symbol involves an oscillating factor. Lebesgue space inequalities are established, which give decay as the oscillation becomes stronger ; this extends the…
How to establish some specific quantitative weighted estimates for the generalized commutator of multilinear fractional singular integral operator $\mathcal{T}_{\eta}^{{\bf b}}$ is the focus of this paper, which is defined by…
Let $({\mathcal X}, d, \mu)$ be a separable metric measure space satisfying the known upper doubling condition, the geometrical doubling condition and the non-atomic condition that $\mu(\{x\})=0$ for all $x\in{\mathcal X}$. In this paper,…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
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 weighted estimates for rough bilinear singular integral operators with kernel $$K(y_1, y_2) = \frac{\Omega((y_1,y_2)/|(y_1,y_2)|)}{|(y_1, y_2)|^{2d}},$$ where $y_i \in \mathbb{R}^{d}$ and $\Omega \in L^{\infty}(S^{2d-1})$ with…
We establish new integral inequalities for the numerical radius and the operator norm of bounded linear operators on Hilbert spaces. Our results refine classical triangle-type and operator matrix inequalities by incorporating convex…
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…
We present a general framework of localized operators, i.e., operators whose matrix coefficients with respect to the Gabor frame are concentrated on the diagonal. We show that localized operators are bounded between modulation spaces, and…