Now showing items 1-20 of 71

    • $A_1$ theory of weights for rough homogeneous singular integrals and commutators 

      Pérez, C.Autoridad BCAM; Rivera-Ríos, I.P.; Roncal, L.Autoridad BCAM (2019)
      Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $\BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \|T_\Omega ...
    • $A_1$ theory of weights for rough homogeneous singular integrals and commutators 

      Pérez, C.Autoridad BCAM; Rivera-Ríos, I.P.; Roncal, L.Autoridad BCAM (2016-07-01)
      Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \|T_\Omega ...
    • Análisis de Fourier en el toro infinito-dimensional 

      Fernández, E. (2019-10-24)
      Se presentan algunos resultados originales de análisis armónico para funciones definidas en el toro infinito, que es el grupo topológico compacto consistente en el producto cartesiano de una familia numerable de toros ...
    • Bilinear Calderón--Zygmund theory on product spaces 

      Li, K.; Martikainen, H.; Vuorinen, E. (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. (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 ...
    • Bilinear Spherical Maximal Functions of Product Type 

      Roncal, L.Autoridad BCAM; Shrivastava, S.; Shuin, K. (2021-08-12)
      In this paper we introduce and study a bilinear spherical maximal function of product type in the spirit of bilinear Calderón–Zygmund theory. This operator is different from the bilinear spherical maximal function considered ...
    • 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 ...
    • A Bilinear Strategy for Calderón’s Problem 

      Ponce Vanegas, F.Autoridad BCAM (2020-05)
      Electrical Impedance Imaging would suffer a serious obstruction if two different conductivities yielded the same measurements of potential and current at the boundary. The Calderón’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. (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. (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.Autoridad BCAM; Rivera-Ríos, I.P. (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. (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. (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 ...
    • Convergence over fractals for the Schrödinger equation 

      Lucà, R.Autoridad BCAM; Ponce-Vanegas, F. (2021-01)
      We consider a fractal refinement of the Carleson problem for the Schrödinger equation, that is to identify the minimal regularity needed by the solutions to converge pointwise to their initial data almost everywhere with ...
    • Correlation imaging in inverse scattering is tomography on probability distributions 

      Caro, P.; Helin, T.; Kujanpää, A.; Lassas, M. (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 ...
    • A Decomposition of Calderón–Zygmund Type and Some Observations on Differentiation of Integrals on the Infinite-Dimensional Torus 

      Fernández, E.; Roncal, L.Autoridad BCAM (2020-02-13)
      In this note we will show a Calder\'on--Zygmund decomposition associated with a function $f\in L^1(\mathbb{T}^{\omega})$. The idea relies on an adaptation of a more general result by J. L. Rubio de Francia in the setting ...
    • Degenerate Poincare-Sobolev inequalities 

      Pérez, C.Autoridad BCAM; Rela, E. (2021)
      Abstract. We study weighted Poincar ́e and Poincar ́e-Sobolev type in- equalities with an explicit analysis on the dependence on the Ap con- stants of the involved weights. We obtain inequalities of the form with different ...
    • 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 ...
    • End-point estimates, extrapolation for multilinear muckenhoupt classes, and applications 

      Li, K.; Martell, J.M.; Martikainen, H.; Ombrosi, S.; Vuorinen, E. (2019)
      In this paper we present the results announced in the recent work by the first, second, and fourth authors of the current paper concerning Rubio de Francia extrapolation for the so-called multilinear Muckenhoupt classes. ...
    • Extensions of the John-Nirenberg theorem and applications 

      Canto, J.; Pérez, C.Autoridad BCAM (2021)
      The John–Nirenberg theorem states that functions of bounded mean oscillation are exponentially integrable. In this article we give two extensions of this theorem. The first one relates the dyadic maximal function to the ...