Dominated bilinear forms and 2-homogeneous polynomials

具有Kadec-Klee性质应用的2-齐次多项式与双线性型的集中定理

Concentration theorems for $2$-homogeneous polynomials and bilinear forms with applications to the Kadec-Klee properties

该研究针对p-凸Banach序列格上的2-齐次多项式与双线性型建立集中定理，推导其Kadec-Klee性质，明确最优条件并拓展至算子空间，还确立了相关张量范数的强次可微性。

Bilinear $θ$-type Calderón-Zygmund operators and its commutator on generalized weighted Morrey spaces over RD-spaces

An RD-space $\mathcal{X}$ is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in $\mathcal{X}$. In this setting, the authors establish the boundedness of bilinear $θ$-type Calderón-Zygmund operator $T_θ$ and its commutator $[b_1,b_2,T_θ]$ generated by the function $b_1,b_2\in BMO(μ)$ and $T_θ$ on generalized weighted Morrey space $\mathcal{M}^{p,ϕ}(ω)$ and generalized weighted weak Morrey space $W\mathcal{M}^{p,ϕ}(ω)$ over RD-spaces.

On the homogeneous ergodic bilinear averages with Möbius and liouville weights

It is shown that the homogeneous ergodic bilinear averages with Möbius or Liouville weight converge almost surely to zero, that is, if $T$ is a map acting on a probability space $(X,\mathcal{A},μ)$, and $a,b \in \mathbb{Z}$, then for any $f,g \in L^2(X)$, for almost all $x \in X$, $${\frac{1}{N}}\sum_{n=1}^{N} ν(n) f(T^{an}x) g(T^{bn}x) \longrightarrow 0, \text{ as } N \longrightarrow +\infty, $$ where $ν$ is the Liouville function or the Möbius function. We further obtain that the convergence almost everywhere holds for the short interval with the help of Zhan's estimation. Also our proof yie…

Dominated polynomials on infinite dimensional spaces

The aim of this paper is to prove a stronger version of a conjecture on the existence of non-dominated scalar-valued m-homogeneous polynomials (m>=3) on arbitrary infinite dimensional Banach spaces.

On Pietsch measures for summing operators and dominated polynomials

We relate the injectivity of the canonical map from $C(B_{E'})$ to $L_p(μ)$, where $μ$ is a regular Borel probability measure on the closed unit ball $B_{E'}$ of the dual $E'$ of a Banach space $E$ endowed with the weak* topology, to the existence of injective $p$-summing linear operators/$p$-dominated homogeneous polynomials defined on $E$ having $μ$ as a Pietsch measure. As an application we fill the gap in the proofs of some results of concerning Pietsch-type factorization of dominated polynomials.

双线性嵌入用于具有一阶项和负势的散度型算子

Bilinear embedding for divergence-form operators with first-order terms and negative potentials

本文研究了具有复系数的二阶散度型算子的双线性嵌入，发展了Carbonaro和Dragičević的理论，并统一了 generalized p-椭圆性条件，证明了H^∞-微分算子在L^p上的有界性和L^p-maximal正则性。