## Search

Now showing items 1-10 of 14

#### Correlation imaging in inverse scattering is tomography on probability distributions

(Inverse Problems, 2018-12-04)

Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments ...

#### Determination of convection terms and quasi-linearities appearing in diffusion equations

(2018-12)

We consider the highly nonlinear and ill posed inverse problem of determining some general expression appearing in the a diffusion equation from measurements of solutions on the lateral boundary. We consider both linear ...

#### Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane

(2018-12)

For electric and magnetic potentials with compact support, we consider the magnetic Schrödinger equation with fixed positive energy. Under a mild additional regularity hypothesis, and with fixed magnetic potential, we show ...

#### Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates

(Mathematische Annalen, 2018-09)

We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that
$$\Big\|\frac{ T(fv)} {v}\Big\|_{L^{1,\infty}(uv)}\le c\, ...

#### Vector-valued operators, optimal weighted estimates and the $C_p$ condition

(Science China Mathematics, 2018-09)

In this paper some new results concerning the $C_p$ classes introduced by Muckenhoupt and later extended by Sawyer, are provided. In particular we extend the result to the full range expected $p>0$, to the weak norm, to ...

#### Weighted norm inequalities for rough singular integral operators

(Journal of Geometric Analysis, 2018-08-17)

In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n-1})$ and the Bochner--Riesz multiplier at the critical index ...

#### On Bloom type estimates for iterated commutators of fractional integrals

(Indiana University Mathematics Journal, 2018-04)

In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from [15]. We give new proofs for those inequalities relying upon a new sparse ...

#### Quantitative weighted estimates for singular integrals and commutators

(2018-02-27)

In this dissertation several quantitative weighted estimates for singular integral op- erators, commutators and some vector valued extensions are obtained. In particular strong and weak type $(p, p)$ estimates, Coifman-Fe ...

#### Bilinear representation theorem

(Transactions of the American Mathematical Society, 2018-01-01)

We represent a general bilinear Calderón--Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators
also admit a simple proof of a sparse bound. In particular, the representation implies a so ...

#### Hölder-Lebesgue regularity and almost periodicity for semidiscrete equations with a fractional Laplacian

(Discrete Contin. Dyn. Syst., 2018)

We study the equations
$
\partial_t u(t,n) = L u(t,n) + f(u(t,n),n); \partial_t u(t,n) = iL u(t,n) + f(u(t,n),n)$
and
$
\partial_{tt} u(t,n) =Lu(t,n) + f(u(t,n),n)$, where $n\in \mathbb{Z}$, $t\in (0,\infty)$, and $L$ ...