اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBesov-ish spaces through atomic decomposition
94
0
0.0
(
0
)
تأليف
Daniel Smania
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We use the method of atomic decomposition to build new families of function spaces, similar to Besov spaces, in measure spaces with grids, a very mild assumption. Besov spaces with low regularity are considered in measure spaces with good grids, and results on multipliers and left compositions are obtained.
قيم البحث
اقرأ أيضاً
In a previous work we introduced Besov spaces $mathcal{B}^s_{p,q}$ defined on a measure spaces with a good grid, with $pin [1,infty)$, $qin [1,infty]$ and $0< s< 1/p$. Here we show that classical Besov spaces on compact homogeneous spaces are example
s of such Besov spaces. On the other hand we show that even Besov spaces defined by a good grid made of partitions by intervals may differ from a classical Besov space, giving birth to exotic Besov spaces.
Some Besov-type spaces $B^{s,tau}_{p,q}(mathbb{R}^n)$ can be characterized in terms of the behavior of the Fourier--Haar coefficients. In this article, the authors discuss some necessary restrictions for the parameters $s$, $tau$, $p$, $q$ and $n$ of
this characterization. Therefore, the authors measure the regularity of the characteristic function $mathcal X$ of the unit cube in $mathbb{R}^n$ via the Besov-type spaces $B^{s,tau}_{p,q}(mathbb{R}^n)$. Furthermore, the authors study necessary and sufficient conditions such that the operation $langle f, mathcal{X} rangle$ generates a continuous linear functional on $B^{s,tau}_{p,q}(mathbb{R}^n)$.
A pair of dual frames with almost exponentially localized elements (needlets) are constructed on $RR_+^d$ based on Laguerre functions. It is shown that the Triebel-Lizorkin and Besov spaces induced by Laguerre expansions can be characterized in terms
of respective sequence spaces that involve the needlet coefficients.
For $mathbb B^n$ the unit ball of $mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^Phi_alpha(mathbb B^n)$, which are generalizations of classical Bergman spaces. We obtain atomic decomposition for functions in the Bergma
n-Orlicz space $mathcal A^Phi_alpha (mathbb B^n)$ where $Phi$ is either convex or concave growth function. We then prove weak factorization theorems involving the Bloch space and a Bergman-Orlicz space and also weak factorization theorems involving two Bergman-Orlicz spaces.
In this article, the authors introduce Besov-type spaces with variable smoothness and integrability. The authors then establish their characterizations, respectively, in terms of $varphi$-transforms in the sense of Frazier and Jawerth, smooth atoms o
r Peetre maximal functions, as well as a Sobolev-type embedding. As an application of their atomic characterization, the authors obtain a trace theorem of these variable Besov-type spaces.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
