Browsing Harmonic Analysis by Title
Now showing items 13-32 of 49
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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 ... -
Flow with $A_\infty(\mathbb R)$ density and transport equation in $\mathrm{BMO}(\mathbb R)$
(Forum of Mathematics, Sigma, 2019-11)We show that, if $b\in L^1(0,T;L^1_{\rm {loc}}(\mathbb R))$ has spatial derivative in the John-Nirenberg space ${\rm{BMO}}(\mathbb R)$, then it generates a unique flow $\phi(t,\cdot)$ which has an $A_\infty(\mathbb R)$ ... -
Global Uniqueness for The Calderón Problem with Lipschitz Conductivities
(Forum of Mathematics, Pi, 2016-01-01)We prove uniqueness for the Calderón problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the three- and four-dimensional cases, this confirms a conjecture of ... -
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 ... -
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 $L$ ... -
Improved A1 − A∞ and related estimates for commutators of rough singular integrals
(Proceedings of the Edinburgh Mathematical Society, 2017)An $A_1-A_\infty$ estimate improving a previous result in [22] for $[b, T_\Omega]$ with $\Omega\in L^\infty(S^{n-1})$ and $b\in BMO$ is obtained. Also a new result in terms of the $A_\infty$ constant and the one ... -
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 ... -
Inverse scattering for a random potential
(2016-05)In this paper we consider an inverse problem for the $n$-dimensional random Schrödinger equation $(\Delta-q+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a ... -
Mixed norm estimates for the Cesàro means associated with Dunkl-Hermite expansions
(Transactions of the American Mathematical Society, 2017)Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with Dunkl--Hermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the Dunkl--Hermite operator ... -
Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer
(Colloquium Mathematicum, 2016-01-01)In this paper we study mixed weighted weak-type inequal- ities for families of functions, which can be applied to study classic operators in harmonic analysis. Our main theorem extends the key result from [CMP2]. -
New bounds for bilinear Calderón-Zygmund operators and applications
(Revista Matemática Iberoamericana, 2016-11-25)In this work we extend Lacey’s domination theorem to prove the pointwise control of bilinear Calderón–Zygmund operators with Dini–continuous kernel by sparse operators. The precise bounds are carefully tracked following ... -
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 ... -
A note on the off-diagonal Muckenhoupt-Wheeden conjecture
(WSPC Proceedings, 2016-07-01)We obtain the off-diagonal Muckenhoupt-Wheeden conjecture for Calderón-Zygmund operators. Namely, given $1 < p < q < \infty$ and a pair of weights $(u; v)$, if the Hardy-Littlewood maximal function satisfies the following ... -
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 ... -
On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians
(Communications on pure and applied analysis, 2019-09)We obtain generalised trace Hardy inequalities for fractional powers of general operators given by sums of squares of vector fields. Such inequalities are derived by means of particular solutions of an extended equation ... -
On pointwise and weighted estimates for commutators of Calderón-Zygmund operators
(Advances in Mathematics, 2017)In recent years, it has been well understood that a Calderón-Zygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar ... -
On sums involving Fourier coefficients of Maass forms for SL(3,Z)
(2016-09-10)We derive a truncated Voronoi identity for rationally additively twisted sums of Fourier coefficients of Maass forms for SL(3,Z), and as an application obtain a pointwise estimate and a second moment estimate for the sums ... -
On the absolute divergence of Fourier series in the infinite dimensional torus
(Colloquium Mathematicum, 2019-03-22)In this note we present some simple counterexamples, based on quadratic forms in infinitely many variables, showing that the implication $f\in C^{(\infty}(\mathbb{T}^\omega)\Longrightarrow\sum_{\bar{p}\in\mathbb{Z}^\inf ... -
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\, ... -
A quantitative approach to weighted Carleson condition
(Concrete Operators, 2017-05-05)Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea for the operator \[ \mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{|Q|}\int_{Q}|f(x)|dx \qquad x\in\mathbb{R}^{n}, \, t \geq0 \] are ...