Related papers: On weighted Ces\`{a}ro function spaces
Let $(\mathcal{X},\rho)$ be a metric space and $\lambda$ be a Borel measure on this space defined on the $\sigma$-algebra generated by open subsets of $\mathcal{X}$; this measure $\lambda$ defines volumes of Borel subsets of $\mathcal{X}$.…
The main purpose of this survey is to gather results on the boundedness of the Bergman projection. First, we shall go over some equivalent norms on weighted Bergman spaces $A^p_\omega$ which are useful in the study of this question. In…
We study embeddings of Besov-Morrey spaces ${\cal N}^{s}_{u,p,q}}({\mathbb R}^d)$ and of Triebel-Lizorkin-Morrey spaces ${\cal E}^{s}_{u,p,q}}({\mathbb R}^d)$ in the limiting cases when the smoothness $s$ equals $s_0=d\max(1/u-p/u,0)$ or…
Compressed Sensing (CS) encompasses a broad array of theoretical and applied techniques for recovering signals, given partial knowledge of their coefficients. Its applications span various fields, including mathematics, physics,…
We obtain an explicit characterization of the $K$-functional of a pair of weighted classical Lorentz spaces of type $S$. We develop a method for obtaining such characterization based on a relation between the desired quantity and the…
The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among others the method is used to give…
Successive divisions of compact metric spaces appear in many different areas of mathematics such as the construction of self-similar sets, Markov partitions associated with hyperbolic dynamical systems, dyadic cubes associated with a…
We define a class of continuous graded graphs similar to the graph of Gelfand--Tsetlin patterns, and describe the set of all ergodic central measures of discrete type on the path spaces of such graphs. The main observation is that an…
The main purpose of this paper is to investigate the behaviour of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed…
In this paper, we study main properties of cone normed spaces, and prove some theorems of weighted means in cone normed spaces.
We characterize those non-negative, measurable functions $\psi$ on $[0,1]$ and positive, continuous functions $\omega_1$ and $\omega_2$ on $\mathbb R^+$ for which the generalized Hardy-Ces\`aro operator $$(U_{\psi}f)(x)=\int_0^1…
We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual space by using, instead of the usual identification via the…
We study a version of the Lebesgue differentiation theorem in which the integral averages are replaced with medians over Busemann--Feller differentiation bases. Our main result gives several characterizations for the differentiation…
A version of the Fr\'echet-Kolmogorov theorem for the compactness of operators in weighted mixed Lebesgue spaces is proved and a corresponding compact extrapolation theory a la Rubio de Francia is developed. Several applications are…
Let $A$ be a general expansive matrix and let $X$ be a ball quasi-Banach function space on $\mathbb R^n$, which supports both a Fefferman--Stein vector-valued maximal inequality and the boundedness of the powered Hardy--Littlewood maximal…
We obtain in this short article the non-asymptotic estimations for the norm of (generalized) Cesaro-Hardy integral operators in the so-called Bilateral Grand Lebesgue Spaces. We also give examples to show the sharpness of these…
We give conditions on the exponent function $p(\cdot)$ that imply the existence of embeddings between grand, small and variable Lebesgue spaces. We construct examples to show that our results are close to optimal. Our work extends recent…
We consider Choquet integrals with respect to dyadic Hausdorff content of non-negative functions which are not necessarily Lebesgue measurable. We study the theory of Lebesgue points. The studies yield convergence results and also a density…
We describe the $(p,q)$ Fock--Carleson measures for weighted Fock--Sobolev spaces in terms of the objects $(s,t)$-Berezin transforms, averaging functions, and averaging sequences on the complex space $\mathbb{C}^n$. The main results show…
We consider a topological integral transform of Bessel (concentric isospectral sets) type and Fourier (hyperplane isospectral sets) type, using the Euler characteristic as a measure. These transforms convert constructible $\zed$-valued…