Harmonic Analysis
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Weighted BMO estimates for singular integrals and endpoint extrapolation in Banach function spaces
(20230501)In this paper we prove sharp weighted BMO estimates for singular integrals, and we show how such estimates can be extrapolated to Banach function spaces. 
Weighted Lorentz spaces: Sharp mixed A<inf>p</inf> − A<inf>∞</inf> estimate for maximal functions
(20230315)We prove the sharp mixed Ap−A∞ weighted estimate for the HardyLittlewood maximal function in the context of weighted Lorentz spaces, namely [Formula presented] where [Formula presented]. Our method is rearrangement free ... 
Extrapolation in general quasiBanach function spaces
(20231115)In this work we prove offdiagonal, limited range, multilinear, vectorvalued, and twoweight versions of the Rubio de Francia extrapolation theorem in general quasiBanach function spaces. We prove mapping properties of ... 
On C0 and C1 continuity of envelopes of rotational solids and its application to 5axis CNC machining
(202310)We study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5axis Computer Numerically Controlled (CNC) machining. A moving cutting tool, conceptualized as a rotational solid, ... 
Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres
(20230101)We establish an asymptotic formula for the number of lattice points in the sets Sh1,h2,h3(λ):={x∈Z+3:⌊h1(x1)⌋+⌊h2(x2)⌋+⌊h3(x3)⌋=λ} with λ∈Z+; where functions h1, h2, h3 are constant multiples of regularly varying functions ... 
On the advectiondiffusion equation with rough coefficients: Weak solutions and vanishing viscosity
(20221101)We deal with the vanishing viscosity scheme for the transport/continuity equation ∂tu+div(ub)=0 drifted by a divergencefree vector field b. Under general Sobolev assumptions on b, we show the convergence of such scheme ... 
Selfimproving PoincaréSobolev type functionals in product spaces
(2021)In this paper we give a geometric condition which ensures that (q, p)Poincar´eSobolev inequalities are implied from generalized (1, 1)Poincar´e inequalities related to L 1 norms in the context of product spaces. ... 
Cones with convoluted geometry that always scatter or radiate
(2021)We investigate fixed energy scattering from conical potentials having an irregular crosssection. The incident wave can be an arbitrary nontrivial Herglotz wave. We show that a large number of such local conical scatterers ... 
The Hajłasz capacity density condition is selfimproving
(2021)We prove a selfimprovement property of a capacity density condition for a nonlocal Haj lasz gradient in complete geodesic spaces. The proof relates the capacity density condition with boundary Poincar´e inequalities, ... 
On quantitative Runge approximation for the time harmonic Maxwell equations.
(2021)Here we derive some results on so called quantitative Runge approximation in the case of the timeharmonic Maxwell equations. This provides a Runge approximation having more explicit quantitative information. We additionally ... 
Sawyertype inequalities for Lorentz spaces
(202206)The HardyLittlewood maximal operator M satisfies the classical Sawyertype 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. ... 
Notes on $H^{\log}$: structural properties, dyadic variants, and bilinear $H^1$$BMO$ mappings
(2022)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 ... 
Polynomial averages and pointwise ergodic theorems on nilpotent groups
(2022)We establish pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two of measurepreserving transformations on $\sigma$finite measure spaces. We also establish ... 
Kato–Ponce estimates for fractional sublaplacians in the Heisenberg group
(20221104)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 LittlewoodPaley ... 
A∞ condition for general bases revisited: complete classification of definitions
(20220527)We refer to the discussion on different characterizations of the A∞ class of weights, initiated by Duoandikoetxea, MartínReyes, 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 Htype groups
(20210310)Recently we have found a couple of errors in our paper entitled An extension problem and trace Hardy inequality for the subLaplacian on $H$type groups, Int. Math. Res. Not. IMRN (2020), no. 14, 42384294. They concern ... 
Maximal operators on the infinitedimensional torus
(20220331)We study maximal operators related to bases on the infinitedimensional 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 ... 
The Frisch–Parisi formalism for fluctuations of the Schrödinger equation
(2022)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 ... 
Rotational smoothing
(20220105)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 ... 
Geometric Harmonic Analysis
(2021)This thesis is the compilation of the results obtained during my PhD, which started in January 2018 and is being completed in the end of 2021. The main matter is divided into ve chapters, Chapters 2 6. Each of these ...