Browsing Harmonic Analysis by Issue Date
Now showing items 21-40 of 54
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Sharp weighted estimates involving one supremum
(Comptes Rendus Mathematique, 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 ... -
Weak and strong $A_p$-$A_\infty$ estimates for square functions and related operators
(Proceedings of the American Mathematical Society, 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} ... -
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 $L$ ... -
Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications
(Adv. Math., 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 ... -
Hardy-type inequalities for fractional powers of the Dunkl-Hermite operator
(Proc. Edinburgh Math. Soc. (2), 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
(Studia Math., 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 ... -
Two-weight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions
(SIAM Journal on Mathematical Analysis, 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 ... -
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 ... -
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
(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 ... -
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 ... -
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 ... -
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
(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 ... -
$A_1$ theory of weights for rough homogeneous singular integrals and commutators
(Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V, 2019)Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $\BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \|T_\Omega ... -
Improved fractional Poincaré type inequalities in John domains
(Arkiv för Matematik, 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 ... -
Sparse bounds for maximal rough singular integrals via the Fourier transform
(Annales de l'institut Fourier, 2019-03-12)We prove a quantified sparse bound for the maximal truncations of convolution-type singular integrals with suitable Fourier decay of the kernel. Our result extends the sparse domination principle by Conde-Alonso, Culiuc, ... -
Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators
(International Mathematics Research Notices, 2019-03-14)Utilising some recent ideas from our bilinear bi-parameter theory, we give an efficient proof of a two-weight Bloom type inequality for iterated commutators of linear bi-parameter singular integrals. We prove that if $T$ ...