Harmonic Analysis
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A note on generalized Fujii-Wilson conditions and BMO spaces
Ombrosi, S.; Pérez, C.
; 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. ... -
Degenerate Poincare-Sobolev inequalities
Pérez, C.; 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 ... -
Regularity of maximal functions on Hardy–Sobolev spaces
Pérez, C.; 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 ... -
Bilinear Spherical Maximal Functions of Product Type
Roncal, L.; 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 ... -
Variation bounds for spherical averages
Beltran, D.; Oberlin, R.; Roncal, L.; 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 -
Pointwise Convergence over Fractals for Dispersive Equations with Homogeneous Symbol
Eceizabarrena, D.; Ponce Vanegas, F. (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 $f\in H^s(\mathbb{R}^n)$ ... -
RESTRICTED TESTING FOR POSITIVE OPERATORS
(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 ... -
Extensions of the John-Nirenberg theorem and applications
Canto, J.; Pérez, C. (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 ... -
Convergence over fractals for the Schrödinger equation
Lucà, 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
(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
(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
(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
(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
(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
(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
(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
(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
(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. (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
(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 ...
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