ﻻ يوجد ملخص باللغة العربية
For a general measure space $(Omega,mu)$, it is shown that for every band $M$ in $L_p(mu)$ there exists a decomposition $mu=mu+mu^{primeprime}$ such that $M=L_p(mu)={fin L_p(mu);f=0 mu^{primeprime}text{-a.e.}}$. The theory is illustrated by an example, with an application to absorption semigroups.
We study the dynamics of the group of isometries of $L_p$-spaces. In particular, we study the canonical actions of these groups on the space of $delta$-isometric embeddings of finite dimensional subspaces of $L_p(0,1)$ into itself, and we show that f
We show that there are $2^{2^{aleph_0}}$ different closed ideals in the Banach algebra $L(L_p(0,1))$, $1<p ot= 2<infty$. This solves a problem in A. Pietschs 1978 book Operator Ideals. The proof is quite different from other methods of producing clos
The aim of this paper is to develop the $L_p$ John ellipsoid for the geometry of log-concave functions. Using the results of the $L_p$ Minkowski theory for log-concave function established in cite{fan-xin-ye-geo2020}, we characterize the $L_p$ John e
In this paper, we investigate the wavelet coefficients for function spaces $mathcal{A}_k^p={f: |(i omega)^khat{f}(omega)|_pleq 1}, kin N, pin(1,infty)$ using an important quantity $C_{k,p}(psi)$. In particular, Bernstein type inequalities associated
The classical Banach space $L_1(L_p)$ consists of measurable scalar functions $f$ on the unit square for which $$|f| = int_0^1Big(int_0^1 |f(x,y)|^p dyBig)^{1/p}dx < infty.$$ We show that $L_1(L_p)$ $(1 < p < infty)$ is primary, meaning that, wheneve