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An error in the paper named in the title $[$ibid., 42-4 (1992)875-889 $]$ is corrected.

Let $H_p$ denote the usual Hardy space of analytic functions on the unit disc $(0\<p\le \infty )$. We prove that for every function $f\in H_1$ there exists a linear operator $T$ defined on $L_1\left(\mathbf{T}\right)$ which is simultaneously bounded from $L_1\left(\mathbf{T}\right)$ to $H_1$ and from $L_{\infty }\left(\mathbf{T}\right)$ to $H_{\infty }$ such that $T\left(f\right)=f$. Consequently, we get the following results $(1\le p_0,p_1\le \infty )$: 1) $(H_{p_0},H_{p_1})$ is a Calderon-Mitjagin couple; 2) for any interpolation functor $F$, we have $F(H_{p_0},H_{p_1})=H\left(F\right(L_{p_0}\left(\mathbf{T}\right),L_{p_1}\left(\mathbf{T}\right)\left)\right)$, where $H\left(F\right(L_{p_0}\left(\mathbf{T}\right),L_{p_1}\left(\mathbf{T}\right)\left)\right)$ denotes the closed subspace of $F\left(L_{p_0}\right(\mathbf{T}),L_{p_1}(\mathbf{T}\left)\right)$ of all functions whose Fourier coefficients vanish...

Let 1 ≤ p ≤ ∞ and let $w_0,w_1$ be two weights on the unit circle such that $log\left(w_0{w}_1^{-1}\right)\in BMO$. We prove that the couple $(H_p\left(w_0\right),H_p\left(w_1\right))$ of weighted Hardy spaces is a partial retract of $(L_p\left(w_0\right),L_p\left(w_1\right))$. This completes previous work of the authors. More generally, we have a similar result for finite families of weighted Hardy spaces. We include some applications to interpolation.

Let $T:L^p\left(\Omega \right)\to L^p\left(\Omega \right)$ be a positive contraction, with $1\<p\<\infty$. Assume that $T$ is analytic, that is, there exists a constant $K\ge 0$ such that $\parallel T^n-T^{n-1}\parallel \le K/n$ for any integer $n\ge 1$. Let $2\<q\<\infty$ and let $v^q$ be the space of all complex sequences with a finite strong $q$-variation. We show that for any $x\in L^p\left(\Omega \right)$, the sequence ${\left(\left[T^n\left(x\right)\right]\left(\lambda \right)\right)}_{n\ge 0}$ belongs to $v^q$ for almost every $\lambda \in \Omega$, with an estimate $\parallel {\left(T^n\left(x\right)\right)}_{n\ge 0}{\parallel }_{L^p\left(v^q\right)}\le C{\parallel x\parallel }_p$. If we remove the analyticity assumption, we obtain an estimate $\parallel {\left(M_n\left(T\right)x\right)}_{n\ge 0}{\parallel }_{L^p\left(v^q\right)}\le C{\parallel x\parallel }_p$, where $M_n\left(T\right)={(n+1)}^{-1}{\sum }_{k=0}^n{T}^k$ denotes the ergodic average of $T$. We also obtain similar results for strongly continuous semigroups ${\left(T_t\right)}_{t\ge 0}$ of positive...