Now showing items 19-38 of 49

    • Improved fractional Poincaré type inequalities in John domains 

      Cejas E.; Drelichman I.; Martínez-Perales J. (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 

      Caro P.; Helin T.; Lassas M. (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 

      Boggarapu P.; Roncal L.; Thangavelu S. (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 

      Ombrosi S.; Pérez C. (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 

      Damián W.; Hormozi M.; Li K. (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 

      Ciaurri Ó.; Roncal L.; Stinga P.R.; Torrea J.L.; Varona J.L. (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 

      Cruz-Uribe D.; Martell J.M.; Pérez C. (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 

      Accomazzo N.; Martínez-Perales J.C.; Rivera-Ríos I.P. (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 

      Boggarapu P.; Roncal L.; Thangavelu S. (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 

      Lerner A. K; Ombrosi S.; Rivera-Ríos I.P. (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) 

      Jääsaari J.; Vesalainen E. V. (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 

      Fernández E.; Roncal L. (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 

      Li K.; Ombrosi S.; Pérez C. (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 

      Rivera-Ríos I.P. (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 ...
    • Quantitative weighted estimates for rough homogeneous singular integrals 

      Hytönen T. P.; Roncal L.; Tapiola O. (Israel Journal of Mathematics, 2017-03-11)
      We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weighted space $L^2(w)$, we obtain a bound ...
    • Quantitative weighted estimates for Rubio de Francia's Littlewood--Paley square function 

      Garg R.; Roncal L.; Shrivastava S. (Journal of Geometric Analysis, 2019-12)
      We consider the Rubio de Francia's Littlewood--Paley square function associated with an arbitrary family of intervals in $\mathbb{R}$ with finite overlapping. Quantitative weighted estimates are obtained for this operator. ...
    • Quantitative weighted estimates for singular integrals and commutators 

      Rivera-Ríos I.P. (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 ...
    • Quantitative weighted mixed weak-type inequalities for classical operators 

      Ombrosi S.; Pérez C.; Recchi J. (Indiana University Mathematics Journal, 2016-06-30)
      We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calderón-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by ...
    • Reconstruction of the Derivative of the Conductivity at the Boundary 

      Ponce-Vanegas F. (2019-08)
      We describe a method to reconstruct the conductivity and its normal derivative at the boundary from the knowledge of the potential and current measured at the boundary. This boundary determination implies the uniqueness ...
    • Reverse Hölder Property for Strong Weights and General Measures 

      Luque T.; Pérez C.; Rela E. (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 ...