We give a proof of commutator estimates for fractional powers of the sublaplacian on the Heisenberg group. Our approach is based on pointwise and $L^p$ estimates involving square fractional integrals and Littlewood--Paley ...

We deal with the vanishing viscosity scheme for the transport/continuity equation ∂tu+div(ub)=0 drifted by a divergence-free vector field b. Under general Sobolev assumptions on b, we show the convergence of such scheme ...

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. ...

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 ...

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 ...

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 ...

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 ...

This article is devoted to a study of the Hardy space $H^{\log} (\mathbb{R}^d)$ introduced by Bonami, Grellier, and Ky. We present an alternative approach to their result relating the product of a function in the real Hardy ...

We consider the solution of the Schrödinger equation $u$ in $\mathbb{R}$ when the initial datum tends to the Dirac comb. Let $h_{\text{p}, \delta}(t)$ be the fluctuations in time of $\int\lvert x \rvert^{2\delta}\lvert ...