Now showing items 63-82 of 100

    • 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 $f\in H^s(\mathbb{R}^n)$ ...
    • Polynomial averages and pointwise ergodic theorems on nilpotent groups 

      Ionescu, A. D.; Magyar, A.; Mirek, M.; Szarek, T.Z.Autoridad BCAM (2022)
      We establish pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two of measure-preserving transformations on $\sigma$-finite measure spaces. We also establish ...
    • Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates 

      Li, K.; Ombrosi, S.; Pérez, C.Autoridad BCAM (2018-09)
      We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that $$\Big\|\frac{ T(fv)} {v}\Big\|_{L^{1,\infty}(uv)}\le c\, ...
    • A quantitative approach to weighted Carleson condition 

      Rivera-Ríos, I.P. (2017-05-05)
      Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea for the operator \[ \mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{|Q|}\int_{Q}|f(x)|dx \qquad x\in\mathbb{R}^{n}, \, t \geq0 \] are ...
    • Quantitative weighted estimates for rough homogeneous singular integrals 

      Hytönen, T.P.; Roncal, L.Autoridad BCAM; Tapiola, O. (2017-03-11)
      We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weighted space $L^2(w)$, we obtain a bound ...
    • Quantitative weighted estimates for Rubio de Francia's Littlewood--Paley square function 

      Garg, R.; Roncal, L.Autoridad BCAM; Shrivastava, S. (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. ...
    • Quantitative weighted estimates for singular integrals and commutators 

      Rivera-Ríos, I.P. (2018-02-27)
      In this dissertation several quantitative weighted estimates for singular integral op- erators, commutators and some vector valued extensions are obtained. In particular strong and weak type $(p, p)$ estimates, Coifman-Fe ...
    • Quantitative weighted mixed weak-type inequalities for classical operators 

      Ombrosi, S.; Pérez, C.Autoridad BCAM; Recchi, J. (2016-06-30)
      We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calderón-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by ...
    • Reconstruction of the Derivative of the Conductivity at the Boundary 

      Ponce Vanegas, F.Autoridad BCAM (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 ...
    • Regularity of maximal functions on Hardy–Sobolev spaces 

      Pérez, C.Autoridad BCAM; Picón, T.; Saari, Olli; Sousa, Mateus (2018-12-01)
      We prove that maximal operators of convolution type associated to smooth kernels are bounded in the homogeneous Hardy–Sobolev spaces H1,p(Rd) when p > d/(d + 1). This range of exponents is sharp. As a by-product of the ...
    • RESTRICTED TESTING FOR POSITIVE OPERATORS 

      Hytönen, T.; Li, K.; Sawyer, E. (2020)
      We prove that for certain positive operators T, such as the Hardy-Littlewood maximal function and fractional integrals, there is a constant D>1, depending only on the dimension n, such that the two weight norm inequality ...
    • Reverse Hölder Property for Strong Weights and General Measures 

      Luque, T.; Pérez, C.Autoridad BCAM; Rela, E. (2016-06-30)
      We present dimension-free reverse Hölder inequalities for strong $A^{\ast}_p$ weights, $1 \le p < \infty$. We also provide a proof for the full range of local integrability of $A^{\ast}_1$ weights. The common ingredient ...
    • Rotational smoothing 

      Caro, P.; Meroño, C.; Parissis, I. (2022-01-05)
      Rotational smoothing is a phenomenon consisting in a gain of regularity by means of averaging over rotations. This phenomenon is present in operators that regularize only in certain directions, in contrast to operators ...
    • Sawyer-type inequalities for Lorentz spaces 

      Pérez, C.Autoridad BCAM; Roure-Perdices, E. (2022-06)
      The Hardy-Littlewood maximal operator M satisfies the classical Sawyer-type estimate ∥Mfv∥L1,∞(uv)≤Cu,v‖f‖L1(u),where u∈ A1 and uv∈ A∞. We prove a novel extension of this result to the general restricted weak type case. ...
    • Scattering with critically-singular and δ-shell potentials 

      Caro, P.; García, A.Autoridad BCAM (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 ...
    • Self-improving Poincaré-Sobolev type functionals in product spaces 

      Cejas, M.E.; Mosquera, C.; Pérez, C.Autoridad BCAM; Rela, E. (2021)
      In this paper we give a geometric condition which ensures that (q, p)-Poincar´e-Sobolev inequalities are implied from generalized (1, 1)-Poincar´e inequalities related to L 1 norms in the context of product spaces. ...
    • Sharp constants in inequalities admitting the Calderón transference principle 

      Kosz, D.Autoridad BCAM (2023)
      The aim of this note is twofold. First, we prove an abstract version of the Calderón transference principle for inequalities of admissible type in the general commutative multilinear and multiparameter setting. Such an ...
    • Sharp estimates for Jacobi heat kernels in conic domains 

      Hanrahan, D.; Kosz, D.Autoridad BCAM (2023)
      We prove genuinely sharp estimates for the Jacobi heat kernels introduced in the context of the multidimensional cone $\mathbb V^{d+1}$and its surface $\mathbb V^{d+1}_0$. To do so, we combine the theory of Jacobi polynomials ...
    • Sharp reverse Hölder inequality for Cp weights and applications 

      Canto, J.Autoridad BCAM (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 ...
    • Sharp weighted estimates involving one supremum 

      Li, K. (2017-07)
      In this note, we study the sharp weighted estimate involving one supremum. In particular, we give a positive answer to an open question raised by Lerner and Moen. We also extend the result to rough homogeneous singular ...