Harmonic Analysis
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Walter Rudin meets Elias M. Stein
(2023)Walter Rudin and Elias M. Stein were giants in the world of mathemat ics. They were loved and admired from students and researchers to teachers and academics, both young and old. They touched many of us through ... 
On the doubling condition in the infinitedimensional setting
(202312)We present a systematic approach to the problem whether a topologically infinitedimensional space can be made homogeneous in the Coifman–Weiss sense. The answer to the question is negative, as expected. Our leading ... 
Sharp estimates for Jacobi heat kernels in conic domains
(2023)We prove genuinely sharp estimates for the Jacobi heat kernels introduced in the context of the multidimensional cone $\mathbb V^{d+1}$and its surface $\mathbb V^{d+1}_0$. To do so, we combine the theory of Jacobi polynomials ... 
Sharp constants in inequalities admitting the Calderón transference principle
(2023)The aim of this note is twofold. First, we prove an abstract version of the Calderón transference principle for inequalities of admissible type in the general commutative multilinear and multiparameter setting. Such an ... 
Boundedness properties of maximal operators on Lorentz spaces
(2023)We study mapping properties of the centered HardyLittlewood maximal operator $\mathcal M$ acting on Lorentz spaces. Given $p \in (1,\infty)$ and a metric measure space $\mathcal X = (X, \rho, \mu)$ we let $\Omega^p_{\rm ... 
Uniform maximal Fourier restriction for convex curves
(2024)We extend the estimates for maximal Fourier restriction operators proved by M\"{u}ller, Ricci, and Wright in \cite{MR3960255} and Ramos in \cite{MR4055940} to the case of arbitrary convex curves in the plane, with constants ... 
Weaktype maximal function estimates on the infinitedimensional torus
(202307)We prove necessary and sufficient conditions for the weak $L^p$ boundedness, for $p\in (1,\infty)$, of a maximal operator on the infinitedimensional torus. In the endpoint case $p=1$ we obtain the same weaktype inequality ... 
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 ...