Zobrazeno 1 - 10
of 17
pro vyhledávání: '"42B10, 42B20"'
Autor:
Zhu, Junjie
Any hypersurface in $\mathbb{R}^{d+1}$ has a Hausdorff dimension of $d$. However, the Fourier dimension depends on the finer geometric properties of the hypersurface. For example, the Fourier dimension of a hyperplane is 0, and the Fourier dimension
Externí odkaz:
http://arxiv.org/abs/2410.09711
Autor:
Goldberg, Michael, Lau, Chun Ho
In this paper, we showed that for suitable $(\beta,p, s,\ell)$ the $\beta$-order fractional derivative with respect to the last coordinate of the Fourier transform of an $L^p(\mathbb{R}^n)$ function is in $H^{-s}$ after restricting to a graph of a fu
Externí odkaz:
http://arxiv.org/abs/2410.06092
Autor:
Zhou, Yue
We consider one-parameter families of quadratic-phase integral transforms which generalize the fractional Fourier transform. Under suitable regularity assumptions, we characterize the one-parameter groups formed by such transforms. Necessary and suff
Externí odkaz:
http://arxiv.org/abs/2409.11201
Autor:
Zhu, Junjie
The notions of Hausdorff and Fourier dimensions are ubiquitous in harmonic analysis and geometric measure theory. It is known that any hypersurface in $\mathbb{R}^{d+1}$ has Hausdorff dimension $d$. However, the Fourier dimension depends on the finer
Externí odkaz:
http://arxiv.org/abs/2401.01455
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
Autor:
Faustino, Nelson
In this paper we exploit the umbral calculus framework to reformulate the so-called discrete Cauchy-Kovalevskaya extension in the scope of hypercomplex variables. The key idea is to consider not only formal power series representation for the underly
Externí odkaz:
http://arxiv.org/abs/1802.08605
Autor:
Ou, Yumeng, Wang, Hong
We obtain improved Fourier restriction estimate for the truncated cone using the method of polynomial partitioning in dimension $n\geq 3$, which in particular solves the cone restriction conjecture for $n=5$, and recovers the sharp range for $3\leq n
Externí odkaz:
http://arxiv.org/abs/1704.05485
Autor:
Dendrinos, Spyridon, Zimmermann, Eugen
We establish $L^p-L^q$ estimates for averaging operators associated to mixed homogeneous polynomial hypersurfaces in $\mathbb{R}^3$. These are described in terms of the mixed homogeneity and the order of vanishing of the polynomial hypersurface and i
Externí odkaz:
http://arxiv.org/abs/1702.03988
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
Autor:
Greenblatt, Michael
A local two-dimensional resolution of singularities theorem and arguments based on the Van der Corput lemma are used to give new estimates for the decay rate of the Fourier transform of a locally defined smooth hypersurface measure in R^3, as well as
Externí odkaz:
http://arxiv.org/abs/1302.4070