Mostrando ítems 1-20 de 63

    • Convergence over fractals for the Schrödinger equation 

      Luca R.; 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 ...
    • Multilinear operator-valued calderón-zygmund theory 

      Di Plinio F.; Li K.; Martikainen H.; Vuorinen E. (Journal of Functional Analysis, 2020)
      We develop a general theory of multilinear singular integrals with operator- valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the R-boundedness ...
    • End-point estimates, extrapolation for multilinear muckenhoupt classes, and applications 

      Li K.; Martell J.M.; Martikainen H.; Ombrosi S.; Vuorinen E. (Trans. Amer. Math. Soc.2020, 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. ...
    • 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 ...
    • Sparse and weighted estimates for generalized Hörmander operators and commutators 

      Ibañez-Firnkorn G.H.; Rivera-Ríos I.P. (Monatshefte für Mathematik, 2019)
      In this paper a pointwise sparse domination for generalized Ho ̈rmander and also for iterated commutators with those operators is provided generalizing the sparse domination result in [24]. Relying upon that sparse domination ...
    • Multilinear singular integrals on non-commutative lp spaces 

      Di Plinio F.; Li K.; Martikainen H.; Vuorinen E. (Springer International Publishing, 2019)
      We prove Lp bounds for the extensions of standard multilinear Calderón- Zygmund operators to tuples of UMD spaces tied by a natural product structure. The product can, for instance, mean the pointwise product in UMD ...
    • The observational limit of wave packets with noisy measurements 

      Caro P.; Meroño C. (2019)
      The authors consider the problem of recovering an observable from certain measurements containing random errors. The observable is given by a pseudodifferential operator while the random errors are generated by a Gaussian ...
    • Scattering with critically-singular and δ-shell potentials 

      Caro P.; García A. (2019)
      The authors consider a scattering problem for electric potentials that have a component which is critically singular in the sense of Lebesgue spaces, and a component given by a measure supported on a compact Lipschitz ...
    • 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 ...
    • Sharp reverse Hölder inequality for Cp weights and applications 

      Canto J. (Journal of Geometric Analysis, 2020)
      We prove an appropriate sharp quantitative reverse Hölder inequality for the $C_p$ class of weights fromwhich we obtain as a limiting case the sharp reverse Hölder inequality for the $A_\infty$ class of weights (Hytönen ...
    • A Bilinear Strategy for Calderón’s Problem 

      Ponce Vanegas F. (Revista Matemática Iberoamericana, 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 Poincaré-type inequalities with applications to weighted improved Poincaré-type inequalities 

      Martinez-Perales J.C. (2020)
      The main result of this paper supports a conjecture by C. P\'erez and E. Rela about the properties of the weight appearing in their recent self-improving result of generalized inequalities of Poincar\'e-type in the Euclidean ...
    • A Decomposition of Calderón–Zygmund Type and Some Observations on Differentiation of Integrals on the Infinite-Dimensional Torus 

      Fernández E.; Roncal L. (Potential Analysis, 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 ...
    • Maximal estimates for a generalized spherical mean Radon transform acting on radial functions 

      Ciaurri Ó.; Nowak A.; Roncal L. (Annali de Matematica Pura et Applicata, 2020)
      We study a generalized spherical means operator, viz.\ generalized spherical mean Radon transform, acting on radial functions. As the main results, we find conditions for the associated maximal operator and its local ...
    • 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 $A_\infty(\mathbb R)$ ...
    • 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 ...
    • 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. ...
    • 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 ...
    • 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 ...
    • 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 ...