我們先定義Besov空間為 $B_{pq}^s$, 滿足 $B_{pq}^s={ f : {
2^{|n|s}||W_n*f||_p } _{ninmathbb{Z}}in ell^q(mathbb{Z})
}$.
當 $s=1$, $p=q $ 時,如果 $f in B_p$ 則$int_mathbb{D}
|f^{(n)}(z)|^p(1-|z|^2)^{2pn-2}dv(z) <+infty$ 且如果 $f in
B_{L,p}$, 則 $int_{mathbb{D}}|f^{'}(z)|^q K(z,z)^{1-q}dv(z)=
O(L(b(e^{-(q-p)^{-1}})))$. 最後我們可以得到以下結果: $ f in
B_{L,p}$, 則 $sum_{n=0}^{infty}
2^{nq}||W_n*f||_p^q=O(L(b(e^{-(q-p)^{-1}})))$.

The Besov class $B_{pq}^s$ is defined by ${ f : {
2^{|n|s}||W_n*f||_p
} _{ninmathbb{Z}}in ell^q(mathbb{Z}) }$. When $s=1$, $p=q
$, we know if $f in B_p$ if and only if
$int_mathbb{D}
|f^{(n)}(z)|^p(1-|z|^2)^{2pn-2}dv(z) <+infty$. It is shown in [5]
that $int_{mathbb{D}}|f^{'}(z)|^q K(z,z)^{1-q}dv(z)=
O(L(b(e^{-(q-p)^{-1}})))$ if $f in B_{L,p}$. In this paper we
will show that $f
in B_{L,p}$ if and only if
$sum_{n=0}^{infty}2^{nq}||W_n*f||_p^q =
O(L(b(e^{-(q-p)^{-1}})))$.

1 Introduction 2
1.1 Smooth Functions. Besov spaces........................2
2 The main result 10
2.1 Symmetrically normed ideals generated by binormalizing sequences................................................10
2.2 Analytic functions on D related to symmetrically normed ideals............................................14

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