Browsing Harmonic Analysis by Issue Date
Now showing items 21-40 of 65
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Weak and strong $A_p$-$A_\infty$ estimates for square functions and related operators
(2017-07)We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound $[w]_{A_p} ... -
Sharp weighted estimates involving one supremum
(2017-07)In this note, we study the sharp weighted estimate involving one supremum. In particular, we give a positive answer to an open question raised by Lerner and Moen. We also extend the result to rough homogeneous singular ... -
Hardy-type inequalities for fractional powers of the Dunkl-Hermite operator
(2018)We prove Hardy-type inequalities for a fractional Dunkl–Hermite operator, which incidentally gives Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use h-harmonic expansions to reduce the ... -
Vector-valued extensions for fractional integrals of Laguerre expansions
(2018)We prove some vector-valued inequalities for fractional integrals defined for several orthonormal systems of Laguerre functions. On the one hand, we obtain weighted $L^p-L^q$ vector-valued extensions, in a multidimensional ... -
Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications
(2018)The analysis of nonlocal discrete equations driven by fractional powers of the discrete Laplacian on a mesh of size $h>0$ \[ (-\Delta_h)^su=f, \] for $u,f:\Z_h\to\R$, $0<s<1$, is performed. The pointwise nonlocal ... -
Two-weight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions
(2018)We investigate a generalized spherical means operator, viz. generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this operator and find precise estimates of ... -
Hölder-Lebesgue regularity and almost periodicity for semidiscrete equations with a fractional Laplacian
(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 $L$ ... -
Bilinear representation theorem
(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 ... -
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 ... -
On Bloom type estimates for iterated commutators of fractional integrals
(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 ... -
Weighted norm inequalities for rough singular integral operators
(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 ... -
Vector-valued operators, optimal weighted estimates and the $C_p$ condition
(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 ... -
Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates
(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\, ... -
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 ... -
Correlation imaging in inverse scattering is tomography on probability distributions
(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 ... -
Scattering with critically-singular and δ-shell potentials
(2019)The authors consider a scattering problem for electric potentials that have a component which is critically singular in the sense of Lebesgue spaces, and a component given by a measure supported on a compact Lipschitz ... -
The observational limit of wave packets with noisy measurements
(2019)The authors consider the problem of recovering an observable from certain measurements containing random errors. The observable is given by a pseudodifferential operator while the random errors are generated by a Gaussian ... -
Improved fractional Poincaré type inequalities in John domains
(2019)We obtain improved fractional Poincaré inequalities in John domains of a metric space $(X, d)$ endowed with a doubling measure $\mu$ under some mild regularity conditions on the measure $\mu$. We also give sufficient ... -
End-point estimates, extrapolation for multilinear muckenhoupt classes, and applications
(2019)In this paper we present the results announced in the recent work by the first, second, and fourth authors of the current paper concerning Rubio de Francia extrapolation for the so-called multilinear Muckenhoupt classes. ...