Results 11 to 20 of about 5,281,258 (136)

Well‐posedness for the fourth‐order Moore–Gibson–Thompson equation in the class of Banach‐space‐valued Hölder‐continuous functions

Mathematical Methods in the Applied Sciences, Volume 46, Issue 2, Page 1928-1937, 30 January 2023., 2023
In this work, we provide a full characterization of well‐posedness in vector‐valued Hölder continuous function spaces for a fourth‐order abstract evolution equation arising from the Moore–Gibson–Thompson equation with memory using operator‐valued Ċα$$ {\dot{C}}^{\alpha } $$‐Fourier multipliers. We illustrate our results by providing an example based on
Marina Murillo‐Arcila
wiley   +1 more source

Lipschitz and Triebel–Lizorkin spaces, commutators in Dunkl setting [PDF]

Nonlinear Analysis, 2023
We first study the Lipschitz spaces $\Lambda_{d}^\beta$ associated with the Dunkl metric, $\beta\in(0,1)$, and prove that it is a proper subspace of the classical Lipschitz spaces $\Lambda^\beta$ on $\mathbb R^N$, as the Dunkl metric and the Euclidean ...
Yongsheng Han, Ming-Yi Lee, Ji Li, B. Wick   +3 more
semanticscholar   +1 more source

Tent Space Approach of Morrey Spaces and Their Application to Duality and Complex Interpolation

Journal of Function Spaces, Volume 2023, Issue 1, 2023., 2023
The aim in this paper is to establish a new duality property of Morrey spaces and to discover the complex interpolation space between Morrey spaces and Lebesgue spaces. For that purpose, a new space Np,qsRn is introduced by using methods of tent spaces. The space generalizes Morrey spaces and Lebesgue spaces.
Takahiro Ono, Andrea Scapellato
wiley   +1 more source

Embeddings between Triebel-Lizorkin Spaces on Metric Spaces Associated with Operators

Analysis and Geometry in Metric Spaces, 2020
We consider the general framework of a metric measure space satisfying the doubling volume property, associated with a non-negative self-adjoint operator, whose heat kernel enjoys standard Gaussian localization.
Georgiadis Athanasios G., Kyriazis George   +1 more
doaj   +1 more source

A parabolic Triebel-Lizorkin space estimate for the fractional Laplacian operator [PDF]

, 2015
In this paper we prove a parabolic Triebel-Lizorkin space estimate for the operator given by \[T^{\alpha}f(t,x) = \int_0^t \int_{{\mathbb R}^d} P^{\alpha}(t-s,x-y)f(s,y) dyds,\] where the kernel is \[P^{\alpha}(t,x) = \int_{{\mathbb R}^d} e^{2\pi ix\cdot\
Minsuk Yang
semanticscholar   +1 more source

Some Notes of Homogeneous Besov–Lorentz Spaces

Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023
In this paper, we consider some properties of homogeneous Besov–Lorentz spaces. First, we get some relationship between B˙p0s,q,B˙p1s,qθ,r and Besov–Lorentz spaces, and then, we obtain the scaling property of B˙p,rs,q and F˙p,rs,q.
Zhenzhen Lou, Seçil Çeken
wiley   +1 more source

Real-Variable Characterizations and Their Applications of Matrix-Weighted Triebel–Lizorkin Spaces [PDF]

Journal of Mathematical Analysis and Applications, 2022
Let $\alpha\in\mathbb R$, $q\in(0,\infty]$, $p\in(0,\infty)$, and $W$ be an $A_p(\mathbb{R}^n,\mathbb{C}^m)$-matrix weight. In this article, the authors characterize the matrix-weighted Triebel-Lizorkin space $\dot{F}_{p}^{\alpha,q}(W)$ via the Peetre ...
Qi Wang, Dachun Yang, Yang-Yang Zhang
semanticscholar   +1 more source

Multiplication in vector‐valued anisotropic function spaces and applications to non‐linear partial differential equations

Mathematische Nachrichten, Volume 295, Issue 9, Page 1709-1754, September 2022., 2022
Abstract We study multiplication as well as Nemytskij operators in anisotropic vector‐valued Besov spaces Bps,ω$B^{s, \omega }_p$, Bessel potential spaces Hps,ω$H^{s, \omega }_p$, and Sobolev–Slobodeckij spaces Wps,ω$W^{s, \omega }_p$. Concerning multiplication we obtain optimal estimates, which constitute generalizations and improvements of known ...
Matthias Köhne, Jürgen Saal
wiley   +1 more source

Traces of some weighted function spaces and related non‐standard real interpolation of Besov spaces

Mathematische Nachrichten, Volume 295, Issue 9, Page 1669-1689, September 2022., 2022
Abstract We study traces of weighted Triebel–Lizorkin spaces Fp,qs(Rn,w)$F^s_{p,q}(\mathbb {R}^n,w)$ on hyperplanes Rn−k$\mathbb {R}^{n-k}$, where the weight is of Muckenhoupt type. We concentrate on the example weight wα(x)=|xn|α$w_\alpha (x) = {\big\vert x_n\big\vert }^\alpha$ when |xn|≤1$\big\vert x_n\big\vert \le 1$, x∈Rn$x\in \mathbb {R}^n$, and ...
Blanca F. Besoy, Dorothee D. Haroske, Hans Triebel   +2 more
wiley   +1 more source