相关论文: The space $L_1(L_p)$ is primary for $1<p<\infty$

We study a function space $JN_p$ based on a condition introduced by John and Nirenberg as a variant of BMO. It is known that $L^p\subset JN_{p}\subsetneq L^{p,\infty}$, but otherwise the structure of $JN_p$ is largely a mystery. Our first…

We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for $p\in [1,\infty]$, every proper subset of $L_p$ is almost Lipschitzly embeddable into a Banach space $X$ if and only if $X$…

Let $L$ be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces $L^{p}(R^{n};X)$ of $X$-valued functions on $R^n$. We characterize Kato's square root estimates $\|\sqrt{L}u\|_{p} \eqsim \|\nabla…

In 1969 Lindenstrauss and Rosenthal showed that if a Banach space is isomorphic to a complemented subspace of an L_p-space, then it is either a script L_p-space or isomorphic to a Hilbert space. This is the motivation of this paper where we…

The class $A_\alpha^p$ consists of those analytic functions $f$ in the unit disc such that \[\|f\|_{\alpha,p}^p := |f(0)|^p+\int_0^1 \left(\frac{d}{dr} M_p^p(r,f)\right) (1-r^2)^{\alpha-1} \,dr < \infty,\] where $M_p^p(r,f)$ is the radial…

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…

For a locally compact group $G$ and $p \in (1,\infty)$, we define $B_p(G)$ to be the space of all coefficient functions of isometric representations of $G$ on quotients of subspaces of $L_p$ spaces. For $p =2$, this is the usual…

For $1<p\le \infty$, we show the existence of a Banach space which is both injectively and surjectively universal for the class of all separable Banach spaces with an equivalent $p$-asymptotically uniformly smooth norm. We prove that this…

This is a continuation of the papers [Kuryakov-Sukochev, JFA, 2015] and [Sadovskaya-Sukochev, PAMS, 2018], in which the isomorphic classification of $L_{p,q}$, for $1< p<\infty$, $1\le q<\infty$, $p\ne q $, on resonant measure spaces, has…

The paper studies Banach spaces satisfying the Littlewood-Paley-Rubio de Francia property LPR_p, 2 \leq p < \infty. The paper shows that every Banach lattice whose 2-concavification is a UMD Banach lattice has this property. The paper also…

We construct Zachary space in $\R^\infty$ and find that this is a Banach space of functions of bounded mean oscillation with order $p, 1\leq p \leq \infty$ containing the function of bounded mean oscillation $BMO[\R_I^\infty]$ as a dense…

We construct a hereditarily indecomposable Banach space with dual isomorphic to $\ell_1$. Every bounded linear operator on this space has the form $\lambda I+K$ with $\lambda$ a scalar and $K$ compact.

The class $M^p$ $(1<p<\infty)$ consists of all holomorphic functions $f$ on the open unit disk $\Bbb D$ for which $$ \int_0^{2\pi}\left(\log^+Mf(\theta)\right)^p\,\frac{d\theta}{2\pi}<\infty, $$ where $Mf(\theta)=\sup_{0\leqslant…

The spaces $W_\alpha$ are the Banach spaces whose duals are isometric to $\ell_1$ and such that the standard basis of $\ell_1$ is $w^*$-convergent to $\alpha\in \ell_1$. The core result of our paper proves that an $\ell_1$-predual $X$…

We study the behaviour of Whitley's thickness constant of a Banach space with respect to $\ell_p$-products and we compute it for classical $L_p$-spaces.

We say that a function $f:[0,1]\rightarrow \R$ is \emph{nowhere $L^q$} if, for each nonvoid open subset $U$ of $[0,1]$, the restriction $f|_U$ is not in $L^q(U)$. For a fixed $1 \leq p <\infty$, we will show that the set $$ S_p\doteq {f \in…

We study subspaces of Orlicz spaces $L_M$ spanned by independent copies $f_k$, $k=1,2,\dots$, of a function $f\in L_M$, $\int_0^1 f(t)\,dt=0$. Any such a subspace $H$ is isomorphic to some Orlicz sequence space $\ell_\psi$. In terms of…

We construct a real sequence $\{\lambda_n\}_{n=1}^{\infty}$ satisfying $\lambda_n = n + o(1)$, and a Schwartz function $f$ on $\mathbb{R}$, such that for any $N$ the system of translates $\{f(x - \lambda_n)\}$, $n > N$, is complete in the…

For each $1\leq p<\infty$ a Banach space of integrable Schwartz distributions is defined by taking the distributional derivative of all functions in $L^p({\mathbb R})$. Such distributions can be integrated when multiplied by a function that…

The list of known Banach spaces whose linear geometry determines the (nonlinear) democracy functions of their quasi-greedy bases to the extent that they end up being democratic, reduces to $c_0$, $\ell_2$, and all separable…