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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 ...
On the doubling condition in the infinite-dimensional setting
(2023-12)
We present a systematic approach to the problem whether a topologically infinite-dimensional space can be made homogeneous in the Coifman–Weiss sense. The answer to the question is negative, as expected. Our leading ...
Extrapolation in general quasi-Banach function spaces
(2023-11-15)
In this work we prove off-diagonal, limited range, multilinear, vector-valued, and two-weight versions of the Rubio de Francia extrapolation theorem in general quasi-Banach function spaces. We prove mapping properties of ...
On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining
(2023-10)
We study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5-axis Computer Numerically Controlled (CNC) machining. A moving cutting tool, conceptualized as a rotational solid, ...
Weak-type maximal function estimates on the infinite-dimensional torus
(2023-07)
We prove necessary and sufficient conditions for the weak- $L^p$ boundedness, for $p\in (1,\infty)$, of a maximal operator on the infinite-dimensional torus. In the endpoint case $p=1$ we obtain the same weak-type inequality ...
Weighted BMO estimates for singular integrals and endpoint extrapolation in Banach function spaces
(2023-05-01)
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
(2023-03-15)
We prove the sharp mixed Ap−A∞ weighted estimate for the Hardy-Littlewood maximal function in the context of weighted Lorentz spaces, namely [Formula presented] where [Formula presented]. Our method is rearrangement free ...
Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres
(2023-01-01)
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 ...
Boundedness properties of maximal operators on Lorentz spaces
(2023)
We study mapping properties of the centered Hardy--Littlewood 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 ...
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 ...