Výsledky vyhledávání - "Shayya, Bassam"

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Mizohata-Takeuchi estimates in the plane

Autor: Shayya, Bassam

Suppose $S$ is a smooth compact hypersurface in $\Bbb R^n$ and $\sigma$ is an appropriate measure on $S$. If $Ef= \hat{fd\sigma}$ is the extension operator associated with $(S,\sigma)$, then the Mizohata-Takeuchi conjecture asserts that $\int |Ef(x)|

Externí odkaz: http://arxiv.org/abs/2208.10305

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A family of fractal Fourier restriction estimates with implications on the Kakeya problem

Autor: Shayya, Bassam

In a recent paper [Ann. of Math. 189 (2019), 837--861], Du and Zhang proved a fractal Fourier restriction estimate and used it to establish the sharp $L^2$ estimate on the Schr\"{o}dinger maximal function in $\Bbb R^n$, $n \geq 2$. In this paper, we

Externí odkaz: http://arxiv.org/abs/2206.12971

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Improved weighted restriction estimates in $\Bbb R^3$

Autor: Shayya, Bassam

Suppose $0 < \alpha \leq n$, $H: \Bbb R^n \to [0,1]$ is a Lebesgue measurable function, and $A_\alpha(H)$ is the infimum of all numbers $C$ for which the inequality $\int_B H(x) dx \leq C R^\alpha$ holds for all balls $B \subset \Bbb R^n$ of radius $

Externí odkaz: http://arxiv.org/abs/2206.06325

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Fourier restriction in low fractal dimensions

Autor: Shayya, Bassam

Publikováno v: Proceedings of the Edinburgh Mathematical Society 64 (2021) 373-407

Let $S \subset \Bbb R^n$ be a smooth compact hypersurface with a strictly positive second fundamental form, $E$ be the Fourier extension operator on $S$, and $X$ be a Lebesgue measurable subset of $\Bbb R^n$. If $X$ contains a ball of each radius, th

Externí odkaz: http://arxiv.org/abs/1905.09513

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Weighted restriction estimates using polynomial partitioning

Autor: Shayya, Bassam

We use the polynomial partitioning method of Guth to prove weighted Fourier restriction estimates in $\Bbb R^3$ with exponents $p$ that range between $3$ and $3.25$, depending on the weight. As a corollary to our main theorem, we obtain new (non-weig

Externí odkaz: http://arxiv.org/abs/1512.03238

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A class of strongly singular integral operators

Autor: Shayya, Bassam Halim.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1996.
Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 45-46).

Externí odkaz: http://catalog.hathitrust.org/api/volumes/oclc/35691507.html

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