Browsing Harmonic Analysis by Title

Now showing items 3-22 of 63

    • 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. (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 ...

    • 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 ...

    • 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 ...

    • 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 ...

    • 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 ...

    • 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 ...

    • 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. (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. ...

    • 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 $A_\infty(\mathbb R)$ ...

    • 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 ...

    • 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 $L$ ...