Now showing items 4-23 of 49

    • Bilinear Calderón--Zygmund theory on product spaces 

      Li K.; Martikainen H.; Vuorinen E. (Journal des Math\'ematiques Pures et Appliqu\'ees, 2019-10)
      We develop a wide general theory of bilinear bi-parameter singular integrals $T$. This includes general Calder\'on--Zygmund type principles in the bilinear bi-parameter setting: easier bounds, like estimates in the Banach ...
    • 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 ...
    • A Bilinear Strategy for Calderón's Problem 

      Ponce-Vanegas F. (2019-08)
      Electrical Impedance Imaging would suffer a serious obstruction if for two different conductivities the potential and current measured at the boundary were the same. The Calder\'on's problem is to decide whether the ...
    • Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators 

      Li K.; Martikainen H.; Vuorinen E. (International Mathematics Research Notices, 2019-03-14)
      Utilising some recent ideas from our bilinear bi-parameter theory, we give an efficient proof of a two-weight Bloom type inequality for iterated commutators of linear bi-parameter singular integrals. We prove that if $T$ ...
    • Bloom type upper bounds in the product BMO setting 

      Li K.; Martikainen H.; Vuorinen E. (Journal of Geometric Analysis, 2019-04-08)
      We prove some Bloom type estimates in the product BMO setting. More specifically, for a bounded singular integral $T_n$ in $\mathbb R^n$ and a bounded singular integral $T_m$ in $\mathbb R^m$ we prove that $$ \| [T_n^1, ...
    • Borderline Weighted Estimates for Commutators of Singular Integrals 

      Pérez C.; Rivera-Ríos I.P. (Israel Journal of Mathematics, 2016-07-01)
      In this paper we establish the following estimate \[ w\left(\left\{ x\in\mathbb{R}^{n}\,:\,\left|[b,T]f(x)\right| > \lambda\right\} \right)\leq \frac{c_{T}}{\varepsilon^{2}}\int_{\mathbb{R}^{n}}\Phi\left(\|b\|_{BMO}\f ...
    • 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, ...
    • 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 ...
    • Correlation imaging in inverse scattering is tomography on probability distributions 

      Caro P.; Helin T.; Kujanpää A.; Lassas M. (Inverse Problems, 2018-12-04)
      Scattering from a non-smooth 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 ...
    • Determination of convection terms and quasi-linearities appearing in diffusion equations 

      Caro P.; Kian Y. (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 $\mathrm{BMO}(\mathbb R)$ 

      Jiang R.; Li K.; Xiao J. (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 

      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 ...
    • Hardy-type inequalities for fractional powers of the Dunkl-Hermite operator 

      Ciaurri Ó.; Roncal L.; Thangavelu S. (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 

      Lizama C.; Roncal L. (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 

      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 ...
    • 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 ...