Browsing Harmonic Analysis by Issue Date
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Sharp weighted estimates involving one supremum
(201707)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 ... 
Weak and strong $A_p$$A_\infty$ estimates for square functions and related operators
(201707)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} ... 
HölderLebesgue 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 $L$ ... 
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 ... 
Hardytype inequalities for fractional powers of the DunklHermite operator
(2018)We prove Hardytype inequalities for a fractional Dunkl–Hermite operator, which incidentally gives Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use hharmonic expansions to reduce the ... 
Twoweight 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 ... 
Vectorvalued extensions for fractional integrals of Laguerre expansions
(2018)We prove some vectorvalued inequalities for fractional integrals defined for several orthonormal systems of Laguerre functions. On the one hand, we obtain weighted $L^pL^q$ vectorvalued extensions, in a multidimensional ... 
Bilinear representation theorem
(20180101)We represent a general bilinear CalderónZygmund 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
(20180227)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, CoifmanFe ... 
On Bloom type estimates for iterated commutators of fractional integrals
(201804)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
(20180817)In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n1})$ and the BochnerRiesz multiplier at the critical index ... 
Vectorvalued operators, optimal weighted estimates and the $C_p$ condition
(201809)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 weaktype estimates
(201809)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\, ... 
Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane
(201812)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 ... 
Determination of convection terms and quasilinearities appearing in diffusion equations
(201812)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 ... 
Correlation imaging in inverse scattering is tomography on probability distributions
(20181204)Scattering from a nonsmooth 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 criticallysingular and δshell 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 ... 
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 ... 
Multilinear singular integrals on noncommutative lp spaces
(2019)We prove Lp bounds for the extensions of standard multilinear Calderón Zygmund operators to tuples of UMD spaces tied by a natural product structure. The product can, for instance, mean the pointwise product in UMD ... 
Sparse and weighted estimates for generalized Hörmander operators and commutators
(2019)In this paper a pointwise sparse domination for generalized Ho ̈rmander and also for iterated commutators with those operators is provided generalizing the sparse domination result in [24]. Relying upon that sparse domination ...