1,720,964 research outputs found
Herz-type Sobolev spaces on domains
Full text linkWe introduce Herz-type Sobolev spaces on domains, which unify and generalize the classical Sobolev spaces. We will give a proof of the Sobolev-type embedding for these function spaces. All these results generalize the classical results on Sobolev spaces. Some remarks on CaffarelliKohnNirenberg inequality are given
Lorentz Herz-type Besov-Triebel-Lizorkin spaces
Full text linkIn this paper, we introduce a new family of function spaces of Besov and Triebel-Lizorkin type. We present the -transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev and Franke-Jewarth embeddings. Also, we establish the smooth atomic, molecular and wavelet decomposition of these function spaces. Characterizations by ball means of differences are given. Finally, we investigate a series of examples which play an important role in the study of function spaces of Besov-Triebel-Lizorkin type
Herz-Sobolev spaces on domains
Full text linkWe introduce Herz-Sobolev spaces, which unify and generalize the classical
Sobolev spaces. We will give a proof of the Sobolev-type embedding for these
function spaces. All these results generalize the classical results on Sobolev
spaces. Some remarks on Caffarelli--Kohn--Nirenberg inequality are given.Comment: 28 page
Mixed-norm Herz-type Besov-Triebel-Lizorkin spaces
Full text linkBased on mixed-norm Herz spaces, Besov and Triebel-Lizorkin spaces, we introduce the so called mixed-norm Herz-type Besov-Triebel-Lizorkin spaces. We present the -transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev, Franke and Jawerth embeddings. Our embeddings extend and improve Sobolev, Franke and Jawerth embeddings of mixed-norm Besov and Triebel-Lizorkin spaces.We add Franke and Jawerth embeddings for such spaces. arXiv admin note: substantial text overlap with arXiv:2406.0270
Caffarelli-Kohn-Nirenberg inequalities on Besov and Triebel-Lizorkin-type spaces
Full text linkWe present some Caffarelli-Kohn-Nirenberg-type inequalities on Herz-type
Besov-Triebel-Lizorkin spaces, Besov-Morrey spaces and Triebel-Lizorkin-Morrey
spaces. More Precisely, we investigate the inequalities \begin{equation*}
\big\|f\big\|_{\dot{k}_{v,\sigma }^{\alpha_{1},r}}\leq
c\big\|f\big\|_{\dot{K}_{u}^{\alpha_{2},\delta }}^{1-\theta
}\big\|f\big\|_{\dot{K}_{p}^{\alpha_{3},\delta_{1}}A_{\beta }^{s}}^{\theta },
\end{equation*} and
\begin{equation*} \big\|f\big\|_{\mathcal{E}_{p,2,u}^{\sigma }}\leq
c\big\|f\big\|_{\mathcal{M}_{\mu }^{\delta }}^{1-\theta
}\big\|f\big\|_{\mathcal{N}_{q,\beta ,v}^{s}}^{\theta }, \end{equation*} with
some appropriate assumptions on the parameters, where is the Herz-type Bessel potential spaces, which are just the
Sobolev spaces if and , and are
Besov or Triebel-Lizorkin spaces if and. To do
these, we study when distributions belonging to these spaces can be interpreted
as functions in . The usual Littlewood-Paley technique,
Sobolev and Franke embeddings are the main tools of this paper. Some remarks on
Hardy-Sobolev inequalities are given.Comment: 36 page
Duality of Triebel-Lizorkin spaces of general weights
Full text linkIn this paper, we identify the duals of Triebel-Lizorkin spaces of
generalized smoothness. In some particular cases these function spaces are just
weighted Triebel-Lizorkin spaces. To do these, we will be working at the level
of sequence spaces. The -transform characterization of these function
spaces in the sense of Frazier and Jawerth, and new weighted version of
vector-valued maximal inequality of Fefferman and Stein are the main tools.Comment: arXiv admin note: substantial text overlap with arXiv:2106.00621,
arXiv:2009.12223, arXiv:2212.0350
Real and complex interpolation of Herz-type Besov-Triebel-Lizorkin spaces
Full text linkThe aim of this paper is twofold. Firstly, we study the real interpolation of Herz-type Besov-Triebel-Lizorkin spaces. Secondly, we present the complex interpolation of Herz-type Besov spaces. As application we give a simple alternative proof of Sobolev embeddings in Herz-type Triebel-Lizorkin spaces α,qFs β, s ∈ , 1 < p, q < ∞, 1 < β ∞ and α2 > α1. These spaces unify and generalize classical Lebesgue spaces of power weights, Sobolev spaces of power weights, Besov spaces and Triebel-Lizorkin spaces.
Communicated Editor: A. Chala.
Manuscript received August. 01st, 2025; revised November 02, 2025; accepted November 06, 2025; published November 11, 2025.Communicated Editor: A. Chala.
Manuscript received August. 01st, 2025; revised November 02, 2025; accepted November 06, 2025; published November 11, 2025
Powers functions in Besov spaces of power weights. Necessary conditions
Full text linkThe aim of this paper is to present some necessary conditions for the
boundedness of the mapping on Besov spaces
equipped with power weights
On the function spaces of general weights
Full text linkThe aim of this paper is twofold. Firstly, we chatacterize the Besov spaces
and the Triebel-Lizorkin spaces
for . Secondly, under some
suitable assumptions on the -admissible weight sequence , we
prove that \begin{equation*}
\dot{A}_{p,q}(\mathbb{R}^{n},\{t_{k}\})=\dot{A}_{p,q}(\mathbb{R}
^{n},t_{j}),\quad j\in \mathbb{Z}, \end{equation*} in the sense of equivalent
quasi-norms, with . Moreover, we find a
necessary and sufficient conditions for the coincidence of the spaces
.Comment: We add Theorem 3.34 and corollaries 3.37 and 3.42. arXiv admin note:
substantial text overlap with arXiv:2009.12223, arXiv:2106.00621,
arXiv:2009.0363
Real interpolation with variable exponent
Full text linkWe present the real interpolation with variable exponent and we prove the basic properties in analogy to the classical real interpolation. More precisely, we prove that under some additional conditions, this method can be reduced to the case of fixed exponent. An application, we give the real interpolation of variable Besov and Lorentz spaces as introduced recently in Almeida and Hästö (J. Funct. Anal. 258 (5) 1628-2655, 2010) and L. Ephremidze et al. (Fract. Calc. Appl. Anal. 11 (4) (2008), 407-420)
- …
