Browsing Harmonic Analysis by Title
Now showing items 32-43 of 43
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Reverse Hölder Property for Strong Weights and General Measures
(Journal of Geometric Analysis, 2016-06-30)We present dimension-free reverse Hölder inequalities for strong $A^{\ast}_p$ weights, $1 \le p < \infty$. We also provide a proof for the full range of local integrability of $A^{\ast}_1$ weights. The common ingredient ... -
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 ... -
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, ... -
Sparse domination theorem for multilinear singular integral operators with $L^{r}$-Hörmander condition
(Michigan Mathematical Journal, 2017-04-01)In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the so-called multilinear $L^{r}$-Hörmander condition, then $T$ can be dominated by multilinear sparse operators. -
Three Observations on Commutators of Singular Integral Operators with BMO Functions
(AWM-Springer Series, Harmonic Analysis, Partial Differentail Equations, Complex Analysis, Banach Spaces, and Operator Theory, 2016-07-01)Three observations on commutators of Singular Integral Operators with BMO functions are exposed, namely 1 - The already known subgaussian local decay for the commutator, namely $\[\frac{1}{|Q|}\left|\left\{x\in Q\, : ... -
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 ... -
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 ... -
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 ... -
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 ... -
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} ... -
Weighted mixed weak-type inequalities for multilinear operators
(Studia Mathematica, 2017)In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let $\vec{w}=(w_1,...,w_m)$ and $\nu = w_1^\frac{1}{m}...w_m^\frac{1}{m}$, the main ... -
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 ...