论文标题
BESOV功能空间中的多元HAAR系统
Multivariate Haar systems in Besov function spaces
论文作者
论文摘要
我们确定所有$ d $维的haar小波系统$ h^d $在单位立方体上$ i^d $是经典的同性恋besov函数空间$ {b} _ {b} _ {p，q，q，1}^S（i^d）一阶$ l_p $平滑度模量。我们获得了张量产品HAAR系统$ \ tilde {h}^d $的类似结果，并表征了$ {b} _ {p，q，q，1}^s（i^d）$的参数范围是$ 0 <p <p <1 $。
We determine all cases for which the $d$-dimensional Haar wavelet system $H^d$ on the unit cube $I^d$ is a conditional or unconditional Schauder basis in the classical isotropic Besov function spaces ${B}_{p,q,1}^s(I^d)$, $0<p,q<\infty$, $0\le s < 1/p$, defined in terms of first-order $L_p$ moduli of smoothness. We obtain similar results for the tensor-product Haar system $\tilde{H}^d$, and characterize the parameter range for which the dual of ${B}_{p,q,1}^s(I^d)$ is trivial for $0<p<1$.
