rest of the paper is organised as follows. We start below with some preliminaries. Then we turn in Section \[section:Wiener\] to some elements of analysis on the Wiener space. Our characterization of the sets $\D^{1,p}$ is given in Section \[section:Malliavin\], and the material on the Malliavin differentiability of BSDEs itself is contained in Section \[section:BSDEs\]. We provide applications and a comparison of the results in Section \[section:applidiscus\]. Finally, we extend our approach to quadratic growth BSDEs in Section \[section:quadratic\].

Preliminaries {#sec:preli}
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Notations
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We fix throughout the paper a time horizon $T>0$ and $d$ a positive integer. For any positive integer $k$, we denote by $\|\cdot\|$ the Euclidian norm in $\R^{k}$ and by $\cdot$ the inner product, without mention of $k$ which will be clear in the context. For any positive integers $n$ and $m$, we identify $\mathbb R^{n\times m}$ with the space of real matrices with $n$ rows and $m$ columns, endowed with the Euclidean norm on $\R^{n\times m}$. Let $M$ be in $\R^{n\times m}$, $1\leq j\leq n$ and $1\leq \ell\leq m$, we denote by $M^{j,:}\in \R^{1\times m}$ (resp. $M^{:,\ell}\in \R^{n,1}$) its $j$-th row (resp. its $\ell$-th column). We set $M^\top\in \R^{m\times n}$ to be the transpose of 