Recent Submissions

  • 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\, ...
  • Weighted norm inequalities for rough singular integral operators 

    Li K.; Pérez C.; Rivera-Ríos I.; Roncal L. (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 ...
  • 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 ...
  • 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 ...
  • Bilinear representation theorem 

    Li K.; Martikainen H.; Ou Y.; Vuorinen E. (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 ...
  • Improved A1 − A∞ and related estimates for commutators of rough singular integrals 

    Rivera-Ríos I.P. (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 ...
  • Weighted mixed weak-type inequalities for multilinear operators 

    Li K.; Ombrosi S.; Picardi B. (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 ...
  • 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 ...
  • 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 ...
  • Weak and strong $A_p$-$A_\infty$ estimates for square functions and related operators 

    Hytönen T.; Li K. (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} ...
  • Sharp weighted estimates involving one supremum 

    Li K. (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 ...
  • 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 ...
  • Sparse domination theorem for multilinear singular integral operators with $L^{r}$-Hörmander condition 

    Li K. (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.
  • A characterization of two weight norm inequality for Littlewood-Paley $g_{\lambda}^{*}$-function 

    Cao M.; Li K.; Xue Q. (Journal of Geometric Analysis, 2017)
    Let $n\ge 2$ and $g_{\lambda}^{*}$ be the well-known high dimensional Littlewood-Paley function which was defined and studied by E. M. Stein, $$g_{\lambda}^{*}(f)(x)=\bigg(\iint_{\mathbb R^{n+1}_{+}} \Big(\frac{t}{t+|x-y ...
  • 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 ...
  • The Calderón problem with corrupted data 

    Caro P.; García A. (Inverse Problems, 2017-01)
    We consider the inverse Calderón problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, ...
  • 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 ...
  • Global Uniqueness for The Calderón Problem with Lipschitz Conductivities 

    Caro P.; Rogers K.M. (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 ...
  • 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 ...
  • 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 ...

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