### Recent Submissions

• #### 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 ...
• #### 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 ...
• #### Maximal operators on the infinite-dimensional torus ﻿

(2022-03-31)
We study maximal operators related to bases on the infinite-dimensional torus $\tom$. {For the normalized Haar measure $dx$ on $\mathbb{T}^\omega$ it is known that $M^{\mathcal{R}_0}$, the maximal operator associated with ...

(2022)
• #### 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 ﻿

(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 ﻿

(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 ...