相关论文: Nikolskii inequality and functional classes on com…
In this article, the authors introduce Besov and Triebel-Lizorkin spaces on spaces of homogeneous type in the sense of Coifman and Weiss, prove that these (in)homogeneous Besov and Triebel-Lizorkin spaces are independent of the choices of…
In this paper, necessary and sufficient conditions on terms of monotone Fourier coefficients for a function to belong to a Nikol'ski\u{\i}--Besov type class are given.
The article examines Nikolskii and Besov spaces with norms defined using $L_p$-averaged mixed moduli of continuity of functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative…
The Grushin spaces, as one of the most important models in the Carnot-Carath\'eodory space, are a class of locally compact and geodesic metric spaces which admit a dilation. Function spaces on Grushin spaces and some related geometric…
We present forms of the classical Riesz-Kolmogorov theorem for compactness that are applicable in a wide variety of settings. In particular, our theorems apply to classify the precompact subsets of the Lebesgue space $L^2$, Paley-Wiener…
We establish the exact-order estimates for the approximation of functions from the Nikol'skii-Besov classes $S^{\boldsymbol{r}}_{1,\theta} B(\mathbb{R}^d)$, $d\geqslant 1$, by entire function exponential type with some restrictions for…
We establish the exact-order estimates of the best approximations of the functions from anisotropic Nikol'skii-Besov classes of several variables by entire functions in the Lebesgue spaces.
We 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*}…
We investigate the boundedness of Fourier multipliers on a compact Lie group when acting on Triebel-Lizorkin spaces. Criteria are given in terms of the H\"ormander-Mihlin-Marcinkiewicz condition. In our analysis, we use the difference…
In this work we study some topological aspects of function spaces arising in Stieltjes differential calculus. Chief among them are compactness results related to the Ascoli-Arzel\`a and Kolmogorov-Riesz theorems, as well as their…
In this article, we study the properties of a class of functional spaces which arise from the investigation of nonlinear differential equations. We establish some integral inequalities then by applying these inequalities, we prove some…
We obtain the exact order estimates of the approximation of the functions of many variables from the generalized Nikol'skii-Besov classes $B^{\Omega}_{p,\theta}(\mathbb{R}^d)$ by sums of de la Vallee Poussin type in the metrics space…
This paper investigates functional inequalities involving Besov spaces and functions of bounded variation, when the underlying metric measure space displays different local and global structures. Particular focus is put on the $L^1$ theory…
In this paper, we introduce a new family of function spaces of Besov and Triebel-Lizorkin type. We present the $\varphi $-transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev and…
In this article, the authors introduce the spaces of Lipschitz type on spaces of homogeneous type in the sense of Coifman and Weiss, and discuss their relations with Besov and Triebel-Lizorkin spaces. As an application, the authors…
We give a sufficient (and, in the case of a compact domain, a necessary) condition for the embedding of Sobolev space of functions with integrable gradient into Besov-Orlicz spaces to be bounded. The condition has a form of a simple…
A basilar property and a useful tool in the theory of Sobolev spaces is the density of smooth compactly supported functions in the space $W^{k,p}(\R^n)$ (i.e. the functions with weak derivatives of orders $0$ to $k$ in $L^p$). On Riemannian…
Teissier problem aims to characterize the equality case of Khovanskii-Teissier type inequality for $(1,1)$-classes on a compact K\"ahler manifold. When each of the involved $(1,1)$-classes is assumed to be nef and big, this problem has been…
The article examines nonisotropic Nikolskii and Besov spaces with norms defined using $L_p$-averaged moduli of continuity of functions of appropriate orders along the coordinate directions, instead of moduli of continuity of known orders…
The article examines Nikolskii and Besov spaces with norms defined using "$L_p$-averaged" mixed moduli of continuity of functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative…