Results 1 to 10 of about 97 (96)

Estimates of bilinear pseudodifferential operators associated to bilinear Hörmander classes in Besov and Triebel-Lizorkin spaces with variable exponents. [PDF]

J Inequal Appl, 2018
In this paper, we give Leibniz-type estimates of bilinear pseudodifferential operators associated to bilinear Hörmander classes in Besov and Triebel–Lizorkin spaces with variable exponents. To obtain the estimate for Triebel–Lizorkin spaces with variable
Xu J, Zhu J.
europepmc   +2 more sources

Local regularity for nonlocal equations with variable exponents

Mathematische Nachrichten, Volume 296, Issue 9, Page 4463-4489, September 2023., 2023
Abstract In this paper, we study local regularity properties of minimizers of nonlocal variational functionals with variable exponents and weak solutions to the corresponding Euler–Lagrange equations. We show that weak solutions are locally bounded when the variable exponent p is only assumed to be continuous and bounded.
Jamil Chaker, Minhyun Kim
wiley   +1 more source

On the trace embedding and its applications to evolution equations

Mathematische Nachrichten, Volume 296, Issue 4, Page 1319-1350, April 2023., 2023
Abstract In this paper, we consider traces at initial times for functions with mixed time‐space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement is that we can allow general interpolation couples.
Antonio Agresti, Nick Lindemulder, Mark Veraar   +2 more
wiley   +1 more source

Fractional‐order operators on nonsmooth domains

Journal of the London Mathematical Society, Volume 107, Issue 4, Page 1297-1350, April 2023., 2023
Abstract The fractional Laplacian (−Δ)a$(-\Delta )^a$, a∈(0,1)$a\in (0,1)$, and its generalizations to variable‐coefficient 2a$2a$‐order pseudodifferential operators P$P$, are studied in Lq$L_q$‐Sobolev spaces of Bessel‐potential type Hqs$H^s_q$. For a bounded open set Ω⊂Rn$\Omega \subset \mathbb {R}^n$, consider the homogeneous Dirichlet problem: Pu=f$
Helmut Abels, Gerd Grubb
wiley   +1 more source

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

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

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

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