arXiv subjects

Georgios Dosidis

Publications and source records attributed to Georgios Dosidis.

6 recordsLinked to original sources

arXiv2024

Bilinear Rough Singular Integrals near the Critical Integrability via Sharp Fourier Multiplier Criteria

We establish boundedness results for bilinear singular integral operators with rough homogeneous kernels whose restriction to the unit sphere belongs to the Orlicz space $L(\log L)^\alpha$. This improves the previously best known condition for boundedness of such bilinear operators obtained in the paper of the first and third authors, and provides estimates close to the conjectured endpoint of integrability suggested by the linear theory. The proof is based on a new sharp boundedness criterion for bilinear Fourier multiplier operators associated with sums of dyadic dilations of a fixed symbol $m_0$, compactly supported away from the origin. This criterion admits the best possible behavior with respect to a modulation of $m_0$ and is intimately connected with sharp shifted square function estimates.

math.CA↗

arXiv2023

Multilinear singular integrals with homogeneous kernels near $L^1$

We obtain the optimal open range of $L^{p_1}(\mathbb R^n)\times\cdots\times L^{p_m}(\mathbb R^n)\to L^p(\mathbb R^n)$ bounds for multilinear singular integral operators with homogeneous kernels of the form $Ω(\frac{y}{|y|})|y|^{-mn}$, where $Ω$ is a function in $L^{q}(\mathbb S^{mn-1})$ with vanishing integral and $q>1$.

math.CA↗

arXiv2022

Nikodym sets and maximal functions associated with spheres

We study spherical analogues of Nikodym sets and related maximal functions. In particular, we prove sharp $L^p$-estimates for Nikodym maximal functions associated with spheres. As a corollary, any Nikodym set for spheres must have full Hausdorff dimension. In addition, we consider a class of maximal functions which contains the spherical maximal function as a special case. We show that $L^p$-estimates for these maximal functions can be deduced from local smoothing estimates for the wave equation relative to fractal measures.

math.CA↗

arXiv2022

On Families between the Hardy-Littlewood and Spherical maximal functions

We study a family of maximal operators that provides a continuous link connecting the Hardy-Littlewood maximal function to the spherical maximal function. Our theorems are proved in the multilinear setting but may contain new results even in the linear case. For this family of operators we obtain bounds between Lebesgue spaces in the optimal range of exponents.

math.CA↗

arXiv2022

The Multilinear Spherical Maximal Function in one dimension

In dimension $n=1$ we obtain $L^{p_1}(\mathbb R) \times\dots\times L^{p_m}(\mathbb R)$ to $L^p(\mathbb R)$ boundedness for the multilinear spherical maximal function in the largest possible open set of indices and we provide counterexamples that indicate the optimality of our results.

math.CA↗

arXiv2019

Multilinear Spherical Maximal Function

In dimensions $n\ge 2$ we obtain $L^{p_1}(\mathbb R^n) \times\dots\times L^{p_m}(\mathbb R^n)$ to $L^p(\mathbb R^n)$ boundedness for the multilinear spherical maximal function in the largest possible open set of indices and we provide counterexamples that indicate the optimality of our results. Moreover, we obtain weak type and Lorentz space estimates as well as counterexamples in the endpoint cases.

math.CA↗