Related papers: Rademacher functions in Morrey spaces

Many of the known complemented subspaces of L_p have realizations as sequence spaces. In this paper a systematic approach to defining these spaces which uses partitions and weights is introduced. This approach gives a unified description of…

Isomorphic classification of symmetric spaces is an important problem related to the study of symmetric structures in arbitrary Banach spaces. This research was initiated in the seminal work of Johnson, Maurey, Schechtman and Tzafriri…

Several new inequalities for moduli of smoothness and errors of the best approximation of a function and its derivatives in the spaces $L_p$, $0<p<1$, are obtained. For example, it is shown that for any $0<p<1$ and $k,\,r\in \mathbb{N}$ one…

Let $L$ be a one to one operator of type $\omega$ having a bounded $H_\infty$ functional calculus and satisfying the $k$-Davies-Gaffney estimates with $k\in{\mathbb N}$. In this paper, the authors introduce the Hardy space…

The goal of this paper is to present an isometric representation of the dual space to Ces\`aro function space $C_{p,w}$, $1<p<\infty$, induced by arbitrary positive weight function $w$ on interval $(0,l)$ where $0<l\leqslant\infty$. For…

In this paper, we analyze multi-dimensional $({\mathrm R}_{X},{\mathcal B})$-almost periodic type functions and multi-dimensional Bohr ${\mathcal B}$-almost periodic type functions. The main structural characterizations and composition…

Let $R$ be the vector of Riesz transforms on $\mathbb{R}^n$, and let $\mu,\lambda \in A_p$ be two weights on $\mathbb{R}^n$, $1 < p < \infty$. The two-weight norm inequality for the commutator $[b, R] : L^p(\mathbb{R}^n;\mu) \to…

We shall investigate the boundedness of the intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces $M^{\Phi,\varphi}_{w}({\mathbb R}^n)$. In all the cases, the conditions for the boundedness are given…

If X is a convex-transitive Banach space and 1\leq p\leq \infty then the closed linear span of the simple functions in the Bochner space L^{p}([0,1],X) is convex-transitive. If H is an infinite-dimensional Hilbert space and C_{0}(L) is…

We prove that a quotient of subspace of $C_p\oplus_pR_p$ ($1\le p<2$) embeds completely isomorphically into a noncommutative $L_p$-space, where $C_p$ and $R_p$ are respectively the $p$-column and $p$-row Hilbertian operator spaces. We also…

Given $1<p<N$ and two measurable functions $V\left( r\right) \geq 0$ and $K\left( r\right) >0$, $r>0$, we define the weighted spaces \[ W=\left\{ u\in D^{1,p}(\mathbb{R}^{N}):\int_{\mathbb{R}^{N}}V\left( \left| x\right| \right) \left|…

We consider Kolmogorov widths of finite sets of functions. Any orthonormal system of $N$ functions is rigid in $L_2$, i.e. it cannot be well approximated by linear subspaces of dimension essentially smaller than $N$. This is not true for…

Let $X$ be a noncomplete metric space satisfying the usual (local) assumptions of a doubling property and a Poincar\'e inequality. We study extensions of Newtonian Sobolev functions to the completion $\widehat{X}$ of $X$ and use them to…

We construct various examples of Sobolev-type functions, defined via upper gradients in metric spaces, that fail to be quasicontinuous or weakly quasicontinuous. This is done with quasi-Banach function lattices $X$ as the function spaces…

In this paper, we show that the expansions of functions from $L^p$-Paley-Wiener type spaces in terms of the prolate spheroidal wave functions converge almost everywhere for $1<p<\infty$, even in the cases when they might not converge in…

A characterization is obtained for those pairs of weights $v$ and $w$ on $\mathbb{R}^2_+$, for which the two--dimensional rectangular integration operator is bounded from a weighted Lebesgue space $L^p_v(\mathbb{R}^2_+)$ to…

Let $(M,F)$ be a $C^\infty$ Finsler manifold, $p\geq 1$ a real number, $k$ a positive integer and $H_k^p (M)$ a certain Sobolev space determined by a Finsler structure $F$. Here, it is shown that the set of all real $C^{\infty}$ functions…

Some new examples of K-monotone couples of the type (X, X(w)), where X is a symmetric space on [0, 1] and w is a weight on [0, 1], are presented. Based on the property of the w-decomposability of a symmetric space we show that, if a weight…

We solve the following three questions concerning surjective linear isometries between spaces of Lipschitz functions $\mathrm{Lip}(X,E)$ and $\mathrm{Lip}(Y,F)$, for strictly convex normed spaces $E$ and $F$ and metric spaces $X$ and $Y$:…

In this paper we make a survey of some recent developments of the theory of Sobolev spaces $W^{1,q}(X,\sfd,\mm)$, $1<q<\infty$, in metric measure spaces $(X,\sfd,\mm)$. In the final part of the paper we provide a new proof of the…