Now showing items 61-72 of 72

    • 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 ...
    • Topics in Harmonic Analysis; commutators and directional singular integrals 

      Accomazzo, N. (2020-03-01)
      This dissertation focuses on two main topics: commutators and maximal directional operators. Our first topic will also distinguish between two cases: commutators of singular integral operators and BMO functions and ...
    • 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 ...
    • A note on generalized Fujii-Wilson conditions and BMO spaces 

      Ombrosi, S.; Pérez, C.Autoridad BCAM; Rela, E.; Rivera-Ríos, I. (2020-07-01)
      In this note we generalize the definition of the Fujii-Wilson condition providing quantitative characterizations of some interesting classes of weights, such as A∞, A∞weak and Cp, in terms of BMO type spaces suited to them. ...
    • Generalized Poincaré-Sobolev inequalities 

      Martínez-Perales, J. (2020-12)
      Poincaré-Sobolev inequalities are very powerful tools in mathematical analysis which have been extensively used for the study of differential equations and their validity is intimately related with the geometry of the ...
    • 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 ...
    • 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 ...
    • Convergence over fractals for the Schrödinger equation 

      Lucà, R.Autoridad BCAM; Ponce Vanegas, F.Autoridad BCAM (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 ...
    • Variation bounds for spherical averages 

      Beltran, D.; Oberlin, R.; Roncal, L.Autoridad BCAM; Stovall, B.; Seeger, A. (2021-06-22)
      We consider variation operators for the family of spherical means, with special emphasis on $L^p\to L^q$ estimates
    • 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 ...
    • Pointwise Convergence over Fractals for Dispersive Equations with Homogeneous Symbol 

      Eceizabarrena, D.; Ponce Vanegas, F.Autoridad BCAM (2021-08-24)
      We study the problem of pointwise convergence for equations of the type $i\hbar\partial_tu + P(D)u = 0$, where the symbol $P$ is real, homogeneous and non-singular. We prove that for initial data $f\in H^s(\mathbb{R}^n)$ ...
    • Discrete Carleman estimates and three balls inequalities 

      Fernández-Bertolin, A.; Roncal, L.Autoridad BCAM; Rüland, A.; Stan, D. (2021-10-16)
      We prove logarithmic convexity estimates and three balls inequalities for discrete magnetic Schrödinger operators. These quantitatively connect the discrete setting in which the unique continuation property fails and the ...