Now showing items 1-20 of 79

• #### $A_1$ theory of weights for rough homogeneous singular integrals and commutators ﻿

(2019)
Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $\BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \|T_\Omega ...
• #### $A_1$ theory of weights for rough homogeneous singular integrals and commutators ﻿

(2016-07-01)
Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \|T_\Omega ...
• #### Análisis de Fourier en el toro infinito-dimensional ﻿

(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 ...
• #### A∞ condition for general bases revisited: complete classification of definitions ﻿

(2022-05-27)
We refer to the discussion on different characterizations of the A∞ class of weights, initiated by Duoandikoetxea, Martín-Reyes, and Ombrosi [Math. Z. 282 (2016), pp. 955–972]. Twelve definitions of the A∞ condition ...
• #### Bilinear Calderón--Zygmund theory on product spaces ﻿

(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 ﻿

(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 ...
• #### Bilinear Spherical Maximal Functions of Product Type ﻿

(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 ...
• #### A Bilinear Strategy for Calderón's Problem ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(2019-04-08)
• #### Convergence over fractals for the Schrödinger equation ﻿

(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 ﻿

(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 ...
• #### Corrigendum to: An extension problem and trace Hardy inequality for the sublaplacian on H-type groups ﻿

(2021-03-10)
Recently we have found a couple of errors in our paper entitled An extension problem and trace Hardy inequality for the sub-Laplacian on $H$-type groups, Int. Math. Res. Not. IMRN (2020), no. 14, 4238--4294. They concern ...
• #### Counterexamples for the fractal Schrödinger convergence problem with an Intermediate Space Trick ﻿

(2021-12-09)
We construct counterexamples for the fractal Schrödinger convergence problem by combining a fractal extension of Bourgain's counterexample and the intermediate space trick of Du--Kim--Wang--Zhang. We confirm that the same ...
• #### A Decomposition of Calderón–Zygmund Type and Some Observations on Differentiation of Integrals on the Infinite-Dimensional Torus ﻿

(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 ...
• #### Degenerate Poincare-Sobolev inequalities ﻿

(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 ...