arXiv subjects

Natalia Accomazzo

Publications and source records attributed to Natalia Accomazzo.

6 recordsLinked to original sources

arXiv2025

Phase retrieval from short-time Fourier transform in LCA groups

We study the short-time Fourier transform phase retrieval problem in locally compact abelian groups. Using probabilistic methods, we show that for a large class of groups $G$ and compact subsets $K\subseteq G$ there exists a window function and a uniformly discrete set in $G\times \widehat{G}$ allowing phase retrieval in $L^2(K)$. We also study the obstructions for STFT phase retrieval on $L^2(G)$, motivating the restriction to compactly supported function spaces.

math.CA↗

arXiv2022

Directional square functions

Quantitative formulations of Fefferman's counterexample for the ball multiplier are naturally linked to square function estimates for conical and directional multipliers. In this article we develop a novel framework for these square function estimates, based on a directional embedding theorem for Carleson sequences and multi-parameter time-frequency analysis techniques. As applications we prove sharp or quantified bounds for Rubio de Francia type square functions of conical multipliers and of multipliers adapted to rectangles pointing along $N$ directions. A suitable combination of these estimates yields a new and currently best-known logarithmic bound for the Fourier restriction to an $N$-gon, improving on previous results of A. Cordoba. Our directional Carleson embedding extends to the weighted setting, yielding previously unknown weighted estimates for directional maximal functions and singular integrals.

math.CA↗

arXiv2021

Weighted Lorentz spaces: sharp mixed $A_p-A_{\infty}$ estimate for maximal functions

We prove the sharp mixed $A_{p}-A_{\infty}$ weighted estimate for the Hardy-Littlewood maximal function in the context of weighted Lorentz spaces, namely \[ \|M\|_{L^{p,q}(w)} \lesssim_{p,q,n} [w]^{\frac1p}_{A_p}[σ]^{\frac1{\min(p,q)}}_{A_{\infty}}, \] where $σ=w^{\frac{1}{1-p}}$. Our method is rearrangement free and can also be used to bound similar operators, even in the two-weight setting. We use this to also obtain new quantitative bounds for the strong maximal operator and for $M$ in a dual setting.

math.CA↗

arXiv2021

Singular integrals along lacunary directions in $\mathbb{R}^n$

A recent result by Parcet and Rogers is that finite order lacunarity characterizes the boundedness of the maximal averaging operator associated to an infinite set of directions in $\mathbb{R}^n$. Their proof is based on geometric-combinatorial coverings of fat hyperplanes by two-dimensional wedges. Seminal results by Nagel-Stein-Wainger relied on geometric coverings of n-dimensional nature. In this article we find the sharp cardinality estimate for singular integrals along finite subsets of finite order lacunary sets in all dimensions. Previous results only covered the special case of the directional Hilbert transform in dimensions two and three. The proof is new in all dimensions and relies, among other ideas, on a precise covering of the n-dimensional Nagel-Stein-Wainger cone by two-dimensional Parcet-Rogers wedges.

math.CA↗

arXiv2018

A characterization of BMO in terms of endpoint bounds for commutators of singular integrals

We provide a characterization of $\mathrm{BMO}$ in terms of endpoint boundedness of commutators of singular integrals. In particular, in one dimension, we show that $\|b\|_{\mathrm{BMO}}\eqsim B$, where $B$ is the best constant in the endpoint $L\log L$ modular estimate for the commutator $[H,b]$. We provide a similar characterization of the space $\mathrm{BMO}$ in terms of endpoint boundedness of higher order commutators of the Hilbert transform. In higher dimension we give the corresponding characterization of $\mathrm{BMO}$ in terms of the first order commutators of the Riesz transforms. We also show that these characterizations can be given in terms of commutators of more general singular integral operators of convolution type.

math.CA↗

arXiv2017

On Bloom type estimates for iterated commutators of fractional integrals

In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from a work of Holmes, Rahm and Spencer. We give new proofs for those inequalities relying upon a new sparse domination that we provide as well in this paper and also in techniques developed in a recent paper due to Lerner, Ombrosi and the third author. We extend as well the necessity established in the work of Holmes, Rahm and Spencer to iterated commutators providing a new proof. As a consequence of the preceding results we recover the one weight estimates in works of Cruz-Uribe and Moen and Bényi, Martell, Moen, Stachura, Torres and establish the sharpness in the iterated case. Our result provides as well a new characterization of the BMO space.

math.CA↗