Zobrazeno 1 - 10
of 2 416
pro vyhledávání: '"$L^p$-boundedness"'
Autor:
Mair, Adam
In this paper we prove a characterization of the $L^p$-to-$L^q$ boundedness of commutators to the Cauchy transform. Our work presents both new results and new proofs for established results. In particular, we show that the Campanato space characteriz
Externí odkaz:
http://arxiv.org/abs/2410.09966
Autor:
Cheng, Jinhua
In this paper, we explore a specific class of bi-parameter pseudo-differential operators characterized by symbols $\sigma(x_1,x_2,\xi_1,\xi_2)$ falling within the product-type H\"ormander {class} $\mathbf{S}^m_{\rho, \delta}$. This classification imp
Externí odkaz:
http://arxiv.org/abs/2409.18413
Autor:
Martini, Alessio, Plewa, Paweł
Let $G=N\rtimes \mathbb{R}$, where $N$ is a Carnot group and $\mathbb{R}$ acts on $N$ via automorphic dilations. Homogeneous left-invariant sub-Laplacians on $N$ and $\mathbb{R}$ can be lifted to $G$, and their sum is a left-invariant sub-Laplacian $
Externí odkaz:
http://arxiv.org/abs/2409.13233
We link Sogge's type $L^p$-estimates for eigenfunctions of the Laplacian on compact manifolds with the problem of providing criteria for the $r$-nuclearity of Fourier integral operators. The classes of Fourier integral operators $I^\mu_{\rho,1-\rho}(
Externí odkaz:
http://arxiv.org/abs/2408.06833
Autor:
Negrín, Emilio R.1,2 (AUTHOR) enegrin@ull.es, Maan, Jeetendrasingh3 (AUTHOR) jsmaan111@rediffmail.com
Publikováno v:
Mathematics (2227-7390). Dec2024, Vol. 12 Issue 24, p3907. 11p.
Autor:
Lee, Gihyun, Lein, Max
A fundamental result in pseudodifferential theory is the Calder\'on-Vaillancourt theorem, which states that a pseudodifferential operator defined from a H\"ormander symbol of order $0$ defines a bounded operator on $L^2(\mathbb{R}^d)$. In this work w
Externí odkaz:
http://arxiv.org/abs/2405.19964
We consider the Laplacian with drift in $\mathbb R^n$ defined by $\Delta_\nu = \sum_{i=1}^n(\frac{\partial^2}{\partial x_i^2} + 2 \nu_i\frac{\partial }{\partial{x_i}})$ where $\nu=(\nu_1,\ldots,\nu_n)\in \mathbb R^n\setminus\{0\}$. The operator $\Del
Externí odkaz:
http://arxiv.org/abs/2403.15232
Let $H = \Delta^2 + V$ be the fourth-order Schr\"odinger operator on $\mathbb{R}^3$ with a real-valued fast-decaying potential $V$. If zero is neither a resonance nor an eigenvalue of $H$, then it was recently shown that the wave operators $W_\pm(H,
Externí odkaz:
http://arxiv.org/abs/2311.06763
In this paper, we study Fourier multipliers on quantum Euclidean spaces and obtain results on their $L^p -L^q$ boundedness. On the way to get these results, we prove Paley, Hausdorff-Young-Paley, and Hardy-Littlewood inequalities on the quantum Eucli
Externí odkaz:
http://arxiv.org/abs/2312.00657
Autor:
Guo, Jingwei, Zhu, Xiangrong
For symbol $a\in S^{n(\rho-1)/2}_{\rho,1}$ the pseudo-differential operator $T_a$ may not be $L^2$ bounded. However, under some mild extra assumptions on $a$, we show that $T_a$ is bounded from $L^{\infty}$ to $BMO$ and on $L^p$ for $2\leq p<\infty$.
Externí odkaz:
http://arxiv.org/abs/2309.10380