Zobrazeno 1 - 10
of 373
pro vyhledávání: '"42B99"'
Autor:
Fraser, Robert
We develop a theory of oscillatory integrals whose phase is given by the trace of a polynomial over an algebraic number field. We present an application to the singular integral for a version of Tarry's problem for algebraic integers.
Comment: 4
Comment: 4
Externí odkaz:
http://arxiv.org/abs/2408.02776
Autor:
Yang, Tongou, Zhong, Yue
We construct a compact set in R2 of measure 0 containing a piece of a parabola of every aperture between 1 and 2. As a consequence, we improve lower bounds for the $L^p$-$L^q$ norm of the corresponding maximal operator for a range of $p$, $q$. Moreov
Externí odkaz:
http://arxiv.org/abs/2408.01917
Autor:
Gressman, Philip T.
Motivated by the testing condition for Radon-Brascamp-Lieb multilinear functionals established in arXiv:2201.12201, this paper is concerned with identifying local conditions on smooth maps $u(t)$ with values in the space of decomposable p-forms on so
Externí odkaz:
http://arxiv.org/abs/2407.18860
Autor:
Li, Jianhui, Yang, Tongou
We put forward a conical principle and a degeneracy locating principle of decoupling. The former generalises the Pramanik-Seeger argument used in the proof of decoupling for the light cone. The latter locates the degenerate part of a manifold and eff
Externí odkaz:
http://arxiv.org/abs/2407.16108
We study the $\varrho$-th order variation seminorm of a general Ornstein--Uhlenbeck semigroup $\left(\mathcal H_t\right)_{t>0}$ in $\mathbb R^n$, taken with respect to $t$. We prove that this seminorm defines an operator of weak type $(1,1)$ with res
Externí odkaz:
http://arxiv.org/abs/2405.00497
We prove that any finite union $P$ of interior-disjoint polytopes in ${\mathbb R}^d$ has the Pompeiu property, a result first proved by Williams [Wil76]. This means that if a continuous function $f$ on $R^d$ integrates to 0 on any congruent copy of $
Externí odkaz:
http://arxiv.org/abs/2404.03405
Autor:
Greenblatt, Michael
We investigate estimating scalar oscillatory integrals by integrating by parts in directions based on $(x_1 \partial_{x_1} f(x) ,..., x_n \partial_{x_n}f(x))$, where $f(x)$ is the phase function. We prove a theorem which provides estimates that are u
Externí odkaz:
http://arxiv.org/abs/2403.12751
We study the Bochner-Riesz problem for the twisted Laplacian $\mathcal L$ on $\mathbb R^2$. For $p\in [1, \infty]\setminus\{2\}$, it has been conjectured that the Bochner-Riesz means $S_\lambda^\delta(\mathcal L) f$ of order $\delta$ converges in $L^
Externí odkaz:
http://arxiv.org/abs/2310.12604
Autor:
Akman, Murat, Mukherjee, Shirsho
We study the Minkowski problem corresponding to the p-harmonic measures and obtain results previously known for harmonic measures due to Jerison. We show that a class of Borel measures on spheres can be prescribed by p-harmonic measures on convex dom
Externí odkaz:
http://arxiv.org/abs/2310.10247
A standard technique for producing monogenic functions is to apply the adjoint quaternionic Fueter operator to harmonic functions. We will show that this technique does not give a complete system in L2 of a solid torus, where toroidal harmonics appea
Externí odkaz:
http://arxiv.org/abs/2308.02965