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Let D be a bounded strictly pseudoconvex domain of ${ℂ}^n$ with smooth boundary. We consider the weighted mixed-norm spaces $A_{\delta ,k}^{p,q}\left(D\right)$ of holomorphic functions with norm $\parallel f{\parallel }_{p,q,\delta ,k}=({\sum }_{\left|\alpha \right|\le k}{ʃ}_0^{r_0}({ʃ}_{\partial D_r}|D^{\alpha }{f|}^{p}d{\sigma }_r{{)}^{q/p}{r}^{\delta q/p-1}dr)}^{1/q}$. We prove that these spaces can be obtained by real interpolation between Bergman-Sobolev spaces $A_{\delta ,k}^p\left(D\right)$ and we give results about real and complex interpolation between them. We apply these results to prove that $A_{\delta ,k}^{p,q}\left(D\right)$ is the intersection of a Besov space $B_s^{p,q}\left(D\right)$ with the space of holomorphic functions on D. Further, we obtain several properties of the mixed-norm...

In this paper we obtain several characterizations of the pointwise multipliers of the space $BMOA$ in the unit ball $B$ of ${ℂ}^n$. Moreover, if $g_1,...,g_m$ are holomorphic functions on $B$, we prove that $M_g\left(f\right)\left(z\right)=\sum _{j=1}^m{g}_j\left(z\right)f_j\left(z\right)$ maps $BMOA\times ...\times BMOA$ onto $BMOA$ if and only if the functions $g_j$ are multipliers of the space $BMOA$ and satisfy $\sum _{j=1}^m\left|g_j\left(z\right)\right|\ge \delta \>0.$

Let D be a bounded strictly pseudoconvex domain of Cⁿ with C ^∞ boundary and Y = {z; u₁(z) = ... = u_l(z) = 0} a holomorphic submanifold in the neighbourhood of D', of codimension l and transversal to the boundary of D. In this work we give a decomposition formula f = u₁f₁ + ... + u_lf_l for functions f of the Bergman-Sobolev space...