Do you want to publish a course? Click here

Wavelets and Triebel type oscillation spaces

298   0   0.0 ( 0 )
 Added by Pengtao Li
 Publication date 2014
  fields
and research's language is English




Ask ChatGPT about the research

We apply wavelets to identify the Triebel type oscillation spaces with the known Triebel-Lizorkin-Morrey spaces $dot{F}^{gamma_1,gamma_2}_{p,q}(mathbb{R}^{n})$. Then we establish a characterization of $dot{F}^{gamma_1,gamma_2}_{p,q}(mathbb{R}^{n})$ via the fractional heat semigroup. Moreover, we prove the continuity of Calderon-Zygmund operators on these spaces. The results of this paper also provide necessary tools for the study of well-posedness of Navier-Stokes equations.



rate research

Read More

We bring a precision to our cited work concerning the notion of Borel measures, as the choice among different existing definitions impacts on the validity of the results.
We study a convergence result of Bourgain--Brezis--Mironescu (BBM) using Triebel-Lizorkin spaces. It is well known that as spaces $W^{s,p} = F^{s}_{p,p}$, and $H^{1,p} = F^{1}_{p,2}$. When $sto 1$, the $F^{s}_{p,p}$ norm becomes the $F^{1}_{p,p}$ norm but BBM showed that the $W^{s,p}$ norm becomes the $H^{1,p} = F^{1}_{p,2}$ norm. Naively, for $p eq 2$ this seems like a contradiction, but we resolve this by providing embeddings of $W^{s,p}$ into $F^{s}_{p,q}$ for $q in {p,2}$ with sharp constants with respect to $s in (0,1)$. As a consequence we obtain an $mathbb{R}^N$-version of the BBM-result, and obtain several more embedding and convergence theorems of BBM-type that to the best of our knowledge are unknown.
Let $Dinmathbb{N}$, $qin[2,infty)$ and $(mathbb{R}^D,|cdot|,dx)$ be the Euclidean space equipped with the $D$-dimensional Lebesgue measure. In this article, via an auxiliary function space $mathrm{WE}^{1,,q}(mathbb R^D)$ defined via wavelet expansions, the authors establish the Riesz transform characterization of Triebel-Lizorkin spaces $dot{F}^0_{1,,q}(mathbb{R}^D)$. As a consequence, the authors obtain the Fefferman-Stein decomposition of Triebel-Lizorkin spaces $dot{F}^0_{infty,,q}(mathbb{R}^D)$. Finally, the authors give an explicit example to show that $dot{F}^0_{1,,q}(mathbb{R}^D)$ is strictly contained in $mathrm{WE}^{1,,q}(mathbb{R}^D)$ and, by duality, $mathrm{WE}^{infty,,q}(mathbb{R}^D)$ is strictly contained in $dot{F}^0_{infty,,q}(mathbb{R}^D)$. Although all results when $D=1$ were obtained by C.-C. Lin et al. [Michigan Math. J. 62 (2013), 691-703], as was pointed out by C.-C. Lin et al., the approach used in the case $D=1$ can not be applied to the case $Dge2$, which needs some new skills.
We characterize the Schauder and unconditional basis properties for the Haar system in the Triebel-Lizorkin spaces $F^s_{p,q}(Bbb R^d)$, at the endpoint cases $s=1$, $s=d/p-d$ and $p=infty$. Together with the earlier results in [10], [4], this completes the picture for such properties in the Triebel-Lizorkin scale, and complements a similar study for the Besov spaces given in [5].
In this article the authors study complex interpolation of Sobolev-Morrey spaces and their generalizations, Lizorkin-Triebel-Morrey spaces. Both scales are considered on bounded domains. Under certain conditions on the parameters the outcome belongs to the scale of the so-called diamond spaces.
comments
Fetching comments Fetching comments
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا