Browsing Harmonic Analysis by Issue Date
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Sharp weighted estimates involving one supremum
(Comptes Rendus Mathematique, 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
(Proceedings of the American Mathematical Society, 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
(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 ... 
Hardytype inequalities for fractional powers of the DunklHermite operator
(Proc. Edinburgh Math. Soc. (2), 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 ... 
Vectorvalued extensions for fractional integrals of Laguerre expansions
(Studia Math., 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 ... 
Twoweight 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, 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
(Indiana University Mathematics Journal, 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
(Journal of Geometric Analysis, 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 ... 
Proof of an extension of E. Sawyer's conjecture about weighted mixed weaktype estimates
(Mathematische Annalen, 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\, ... 
Vectorvalued operators, optimal weighted estimates and the $C_p$ condition
(Science China Mathematics, 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 ... 
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 ... 
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 ... 
Correlation imaging in inverse scattering is tomography on probability distributions
(Inverse Problems, 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 ... 
$A_1$ theory of weights for rough homogeneous singular integrals and commutators
(Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V, 2019)Quantitative $A_1A_\infty$ 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, 20190312)We prove a quantified sparse bound for the maximal truncations of convolutiontype singular integrals with suitable Fourier decay of the kernel. Our result extends the sparse domination principle by CondeAlonso, Culiuc, ... 
Bloom type inequality for biparameter singular integrals: efficient proof and iterated commutators
(International Mathematics Research Notices, 20190314)Utilising some recent ideas from our bilinear biparameter theory, we give an efficient proof of a twoweight Bloom type inequality for iterated commutators of linear biparameter singular integrals. We prove that if $T$ ...